https://eeedg.ca eeedg Wed, 11 Jan 2023 19:34:57 +0000 https://eeedg.ca en https://eeedg.ca/landing-page Tue, 31 Aug 2021 02:41:32 +0000 eeedg https://eeedg.ca/landing-page Eric De Giuli // algorithmic art statement //&nbsp; twitter // instagram eric.degiuli@gmail.com I am an algorithmic artist making work as executable html files, accessible anywhere and by anyone. Recent works run live, evolve forever in your browser, and are interactive. For examples see Atlas 10, Atlas 13, Atlas 171,&nbsp;cathedral study 39, Calian 6, Calian 24 (links open in a new tab) New: via&nbsp;SOLOS at Verse zero (broken symmetry)from a blank slate that does not know left from righta tiny spark ignites a flameeventually engulfing the entire screen.zero is always initiated with an empty canvas,yet tiny errors at the level of machine precision are amplified until all vestige of the original simplicity is lost, forever. zero is a meditation on the growth of form, an answer to the question: from the simplicity of natural law, how does the world become so complex? <img width="3024" height="1646" width_o="3024" height_o="1646" data-src="https://freight.cargo.site/t/original/i/73466cbcdf3ef9a367f667fc62ea5f55aa8f30bf0aafd3f290068a3126d528b7/Zero-123000457.png" data-mid="237324948" border="0" src="https://freight.cargo.site/w/1000/i/73466cbcdf3ef9a367f667fc62ea5f55aa8f30bf0aafd3f290068a3126d528b7/Zero-123000457.png" /> WORKS available as NFT collections:&nbsp;( inquire to purchase NFTs from the artist’s collection or order archival inkjet prints )&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 2025/08. Zero (broken symmetry)** on SOLOS at Verse&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 2024/10. Pax* on Art Blocks Studio 2024/06.&nbsp;Interaction Studies&nbsp;1 on ENSEMBLE 2023/11. &nbsp; Atlas *&nbsp; 2023/05. cathedral study * at PROOF 2023/03. Calian * at Art Blocks&nbsp; 2022/11.&nbsp; &nbsp;Glass Study s For the tribute to Herbert W. Franke 2022/08.&nbsp;Glass&nbsp;2s at Art Blocks 2022/03.&nbsp;Mazinaw&nbsp;2s at Art Blocks 2022/01. &nbsp;Stitched&nbsp;$32021/12.&nbsp; impossible cathedrals&nbsp;$4s 2021/09. Spectral Beings #5m2021/09. Snapped&nbsp;$s 2021/09. alien codex #s 2021/08. alien tongues #s 2001-2006. generative landscapes WRITING &amp; SPEAKING:&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; 2025. From Atlas to Zero, Verse. Written interview with sssluke &nbsp;&nbsp; &nbsp; &nbsp; &nbsp;2025. Eric De Giuli: breaking symmetry. Verse Talks. Podcast interview (spotify)&nbsp; 2024. 70 years of Art vs Science. Generative Art Summit, Akademie der Kunst, Berlin. 20 minute talk covering the manifold connections between art and science. 2024. 70 years of Art vs Science. Generative Art Summit, Akademie der Kunst, Berlin. Panel discussion with William Latham. 2024. Interaction Studies on ENSEMBLE: 7 min video including interview 2023. Essay by Duncan Cooper on Atlas: “A map of everything” at Outland2023.&nbsp;On Calian2022.&nbsp;The visual interpretation of quantum mechanics. 2022.&nbsp;Emergence: an essay2021. Spectral Beings: morphogenesis SELECTED EXHIBITIONS:&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2025/10. Calian in FuturaCanvas, Seoul, KR &nbsp; &nbsp; &nbsp; &nbsp;2024/07. Atlas in Code - Kunst - Konstruktionen, Städische Galerie Wolfsburg, Germany&nbsp; &nbsp; &nbsp; &nbsp;2024/04. Atlas in Dimensions of Digitization, New Haven, CT&nbsp; &nbsp; &nbsp; &nbsp;2023/09. cathedral study at The Foundry, Los Angeles CA&nbsp; &nbsp; &nbsp; &nbsp;2023/09. Calian in Collēctīvus: Computation, Consciousness, and Collective Memory, Art Blocks Gallery, Marfa TX &nbsp; &nbsp; &nbsp; &nbsp;2022/11. Glass at The Boiler, Brooklyn NY &nbsp; &nbsp; &nbsp; &nbsp;2022/06. Spectral Beings, Alien Codex in Odyssey at The Boiler, Brooklyn NY ** js + glsl. code on-chain and executable via Verse API. Standard collection delivered by IPFS * js + glsl. code on-chain, executable via Art Blocks (Engine) API $ Released anonymously as pepe xyz# Released as eeedg s Still image&nbsp; m Video clip (.mp4) 1. js + glsl. executable html on IPFS 2. js + p5.js. p5.js script on-chain, executable via Art Blocks API 3. js + p5.js. executable html on IPFS via fxhash. Individual pieces can be minted on Ethereum by request4. js + p5.js. executable html on IPFS via fxhash. 5. js + p5.js. p5.js script on-chain for archival purposes there are no artifacts. there are only interpretations Pax. Navigate a strange world of dissolving forms&nbsp; <img width="1512" height="945" width_o="1512" height_o="945" data-src="https://freight.cargo.site/t/original/i/dd4389b6f18c9a09d2bfa5ca2ceca2c67591fa5a6b266965501a69697b9617e2/Pax-0xc51bdd22174283ed6eea0f4c389d631dfafa21f74d4c1babf79355e963a8e0a4-321098.200-0.2726-0.6908-0.6697-0.0423-1.8493-3.5933--0.1531-0.7184--0.6786-0.339-0.339-1.649.jpg" data-mid="220354570" border="0" src="https://freight.cargo.site/w/1000/i/dd4389b6f18c9a09d2bfa5ca2ceca2c67591fa5a6b266965501a69697b9617e2/Pax-0xc51bdd22174283ed6eea0f4c389d631dfafa21f74d4c1babf79355e963a8e0a4-321098.200-0.2726-0.6908-0.6697-0.0423-1.8493-3.5933--0.1531-0.7184--0.6786-0.339-0.339-1.649.jpg" /> GLASS: at Artblocks See: INTRO HERE&nbsp; <img width="1920" height="2400" width_o="1920" height_o="2400" data-src="https://freight.cargo.site/t/original/i/3ad1f25b7194ad7cb9094e08412e67c8a12e7546acf1a11cddea04b994fc4e37/344000217.jpg" data-mid="164383541" border="0" src="https://freight.cargo.site/w/1000/i/3ad1f25b7194ad7cb9094e08412e67c8a12e7546acf1a11cddea04b994fc4e37/344000217.jpg" /> MAZINAW: at Artblocks See: Emergence: an essay <img width="2450" height="1960" width_o="2450" height_o="1960" data-src="https://freight.cargo.site/t/original/i/f44676e4ace2ce2109602b8e7da1529d5c26daaed327369ff7899229ca8581dd/Mazinaw_58.jpg" data-mid="164383502" border="0" src="https://freight.cargo.site/w/1000/i/f44676e4ace2ce2109602b8e7da1529d5c26daaed327369ff7899229ca8581dd/Mazinaw_58.jpg" /> See twitter / instagram for work-in-progress spectral beings 888/888&nbsp; [_] <img width="600" height="600" width_o="600" height_o="600" data-src="https://freight.cargo.site/t/original/i/e7e98b2f6a1134026b2555eecba42279b23c0a516f1ed94404d0392e3981367c/SB_812.gif" data-mid="120138708" border="0" data-scale="49" src="https://freight.cargo.site/w/600/i/e7e98b2f6a1134026b2555eecba42279b23c0a516f1ed94404d0392e3981367c/SB_812.gif" /><img width="600" height="600" width_o="600" height_o="600" data-src="https://freight.cargo.site/t/original/i/962d207526250d9c58936d0e253c66b699a0e5cba7f2f79336ecfe8e8de4d467/SB_803.gif" data-mid="120138839" border="0" data-scale="49" src="https://freight.cargo.site/w/600/i/962d207526250d9c58936d0e253c66b699a0e5cba7f2f79336ecfe8e8de4d467/SB_803.gif" /> alien tongues 50/50 <img width="774" height="774" width_o="774" height_o="774" data-src="https://freight.cargo.site/t/original/i/5d45f85568dc483390d825c4bb0563390df82f6564bde0787be2e3958a9a6684/051_crop.png" data-mid="117710807" border="0" data-scale="99" src="https://freight.cargo.site/w/774/i/5d45f85568dc483390d825c4bb0563390df82f6564bde0787be2e3958a9a6684/051_crop.png" /> alien codex 200/200 <img width="1378" height="1378" width_o="1378" height_o="1378" data-src="https://freight.cargo.site/t/original/i/76fd95a697822c71c11bf144ec07921bfe890a4f9c058fd24b3acd03d4a85c9e/NFS1329880399..png" data-mid="117710847" border="0" src="https://freight.cargo.site/w/1000/i/76fd95a697822c71c11bf144ec07921bfe890a4f9c058fd24b3acd03d4a85c9e/NFS1329880399..png" /> https://eeedg.ca/Calian-1 Wed, 11 Jan 2023 19:34:57 +0000 eeedg https://eeedg.ca/Calian-1 On Calian Among their extraordinary features, living systems balance the seemingly contradictory requirements of robustness, which entails a return to a stable state, and flexibility, which requires a family of states matched to external inputs. How these properties arise from inanimate matter is one of the leading questions faced by contemporary physicists: how can we describe life as a state of matter, and when does it arise? In my research I study this in the context of chemical reaction networks, having in mind Darwin’s ‘warm little pond’ that presumably led, by some unknown sequence of events, to all life on Earth today. The surprising result of my research is that it is crucial that the component parts of life are small. Specifically, the chemical species cannot have too large a number of molecules. The reason is that large chemical reaction networks are too stable: they are robust, but they cannot jump between a variety of states, and therefore are inflexible. This result does not depend on the details of reactions, but only on fundamental physical laws (1). In contrast, when the number of molecules is small, it is possible for systems to jump between different states, allowing flexibility. How such systems regain robustness is then a mystery. Living matter must solve this robustness vs flexibility dilemma.&nbsp; <img width="1968" height="1968" width_o="1968" height_o="1968" data-src="https://freight.cargo.site/t/original/i/95a37df225499e16dbc0515e6ae47151e9c667b56a1a746761bda840927d8273/Calian-123000995.jpg" data-mid="164403443" border="0" src="https://freight.cargo.site/w/1000/i/95a37df225499e16dbc0515e6ae47151e9c667b56a1a746761bda840927d8273/Calian-123000995.jpg" />‘liquid circuit,’ Calian. 2023. These considerations motivate Calian. A simulation of so-called reaction-diffusion dynamics (2) would generally lead to well-developed stable states, without flexibility. At the opposite extreme, cellular automata, which have a discrete, unsmooth dynamics, can host a great variety of patterns, but they are utterly unpredictable. Calian walks the line between these extremes. The smooth dynamics of reaction-diffusion is subtlely broken in several distinct ways, each leading to new structures that are expressed across the Calian collection. First, the dynamics is made sensitive to very small amounts of the competing chemical species. Coupled with the underlying discrete grid on which they live, this allows us to evade the aforementioned theorem that would restrict the dynamics. In other words, the simulation is not simply integration of differential equations. Second, instead of simple diffusion -- smoothing out of inhomogeneities -- Calian allows both anti-diffusion, which leads to instabilities and therefore complexity, and anisotropic diffusion, that is diffusion that depends on the direction. This allows patterns that can have square or diamond edges, growth along cardinal directions, and other phenomena.&nbsp; &nbsp; Third, the reactions are catalyzed by random nutrient fields that move across the canvas and evolve in time. Sometimes they lead to tornado-like vortices shearing the medium. <img width="1523" height="1523" width_o="1523" height_o="1523" data-src="https://freight.cargo.site/t/original/i/312d02711255fd2f5c9d501730c4ab89288b7db8f720f7981845ff9c5bc16c58/LIFE-123000554_sml_A.jpg" data-mid="164560465" border="0" data-scale="92" src="https://freight.cargo.site/w/1000/i/312d02711255fd2f5c9d501730c4ab89288b7db8f720f7981845ff9c5bc16c58/LIFE-123000554_sml_A.jpg" /> <img width="1526" height="1526" width_o="1526" height_o="1526" data-src="https://freight.cargo.site/t/original/i/37cf5f2d0f711590e45daba97e9244f5c379bf0ad041d83add6543a93e0b2eef/LIFE-123000554_sml_B.jpg" data-mid="164560466" border="0" data-scale="91" src="https://freight.cargo.site/w/1000/i/37cf5f2d0f711590e45daba97e9244f5c379bf0ad041d83add6543a93e0b2eef/LIFE-123000554_sml_B.jpg" /> <img width="1530" height="1530" width_o="1530" height_o="1530" data-src="https://freight.cargo.site/t/original/i/02d61d414d0c38b0250cf42202320897dfcb879e70d69f883a11e596a2356094/LIFE-123000554_sml_C.jpg" data-mid="164560467" border="0" data-scale="91" src="https://freight.cargo.site/w/1000/i/02d61d414d0c38b0250cf42202320897dfcb879e70d69f883a11e596a2356094/LIFE-123000554_sml_C.jpg" />‘bouquet’ <img width="2082" height="2082" width_o="2082" height_o="2082" data-src="https://freight.cargo.site/t/original/i/652ab673466debebdfb7c8cd5cc7d7cb5e715f262e58c595732baee433f946ee/LIFE-123000159.jpg" data-mid="164560384" border="0" src="https://freight.cargo.site/w/1000/i/652ab673466debebdfb7c8cd5cc7d7cb5e715f262e58c595732baee433f946ee/LIFE-123000159.jpg" />‘the forest path to the spring’&nbsp; Altogether the key parameters controlling the dynamics span about 20 dimensions. Each style, of which there are 15, starts at a specific point in this 20 dimensional space, and is associated to a fixed palette. The styles have distinct personalities, variously highlighting or suppressing the features described above. Some styles, such as ‘constellation’ and ‘nocturne’, gently develop into detailed point-like structures; while others, like ‘bouquet’ and ‘the forest path to the spring’, dazzle with instability and growth. Some, like ‘kind of blue’ and ‘liquid circuit’, show explicitly the tension between organic and digital. Species can either grow smoothly (’classical’) or in discrete jumps (’quantum’).&nbsp; The aim of all these ingredients is to make Calian a dynamic complex system that evolves eternally and can be explored at different scales (by zooming and panning). I encourage the viewer to spend time with each piece, both watching it develop in place, and seeing how the ecosystem reacts as you interact with it. Is it alive? How do you decide? (1) The technical result is that chemical reaction networks in the large-particle-number deterministic limit have a function that never increases in time ( a Lyapunov function ), so they cannot hop between multiple attractors. See e.g.&nbsp;Eric De Giuli and Camille Scalliet 2022 J. Phys. A: Math. Theor. 55 474002 (2) A class of models in which nonlinear reactions lead to growth and instability while diffusion (smoothing) tends to stabilize the system. Turing proposed one in 1952 to explain (among other things) how animals get stripes and spots; more recently the Gray-Scott model (1983) has been extensively studied. Calian extends the Gray-Scott model. https://eeedg.ca/page-1 Wed, 10 Aug 2022 20:50:16 +0000 eeedg https://eeedg.ca/page-1 The visual interpretation of quantum mechanics Glass is a visual and sensory exploration of the boundary between the quantum and classical worlds. Two levels of reality, which for us are vastly separated in scale, are brought close together so that they may be perceived simultaneously.&nbsp;<img width="2000" height="2500" width_o="2000" height_o="2500" data-src="https://freight.cargo.site/t/original/i/284385d7e768c32f43e154f690936d5c87b8911b1b093178d68b3be0946ed53a/Glass_marbles_sml.jpg" data-mid="150122641" border="0" src="https://freight.cargo.site/w/1000/i/284385d7e768c32f43e154f690936d5c87b8911b1b093178d68b3be0946ed53a/Glass_marbles_sml.jpg" /> https://eeedg.ca/page-2 Thu, 11 Aug 2022 00:53:41 +0000 eeedg https://eeedg.ca/page-2 To experience Glass you must look at its microscopic world.<img width="1456" height="1456" width_o="1456" height_o="1456" data-src="https://freight.cargo.site/t/original/i/99b5f5e19cbbb1f43def90aa7a2325fb30ff34a4f6d11ddd24a55a45cb08dda4/Glass_marbles_sml_crop.jpg" data-mid="150122666" border="0" src="https://freight.cargo.site/w/1000/i/99b5f5e19cbbb1f43def90aa7a2325fb30ff34a4f6d11ddd24a55a45cb08dda4/Glass_marbles_sml_crop.jpg" /> Panes of transparent glass intersect and overlap. Starting anywhere, you can interpret what you see as part of a three dimensional object, but whose orientation is unclear. As your eyes continue along a path, you will find edges that force the panes to take a specific orientation. But if you try to extrapolate, you find contradictions: panes that looked horizontal now seem to be vertical, or vice versa. On a larger scale, it is impossible to perceive this scene as a definite physical object that can live in three dimensions.&nbsp; https://eeedg.ca/page-3 Thu, 11 Aug 2022 01:08:59 +0000 eeedg https://eeedg.ca/page-3 Remarkably, what you are experiencing maps onto a typical quantum mechanical system, like our universe. In a modern extension of the Copenhagen interpretation of quantum mechanics*, the characteristic feature of quantum reality is that different observers can have inconsistent histories about what happens in the world. There is fundamentally no single objective reality on which all observers will agree.**&nbsp; Glass is based on the premise that while here, the top group of panes looks vertical and the bottom group looks horizontal, ...<img width="1024" height="768" width_o="1024" height_o="768" data-src="https://freight.cargo.site/t/original/i/c6b734b2d35008913e3606937276a0d3bc67e958fd310b1d2cc68e78db07a800/Glass.001.jpeg" data-mid="150125407" border="0" src="https://freight.cargo.site/w/1000/i/c6b734b2d35008913e3606937276a0d3bc67e958fd310b1d2cc68e78db07a800/Glass.001.jpeg" />... if we see only a small subset of these clusters, we cannot distinguish them.<img width="1024" height="768" width_o="1024" height_o="768" data-src="https://freight.cargo.site/t/original/i/462b779735c53ff2eead74e453ab347e57742141ad3016b63223fe8fc237ee8e/Glass.002.jpeg" data-mid="150131512" border="0" src="https://freight.cargo.site/w/1000/i/462b779735c53ff2eead74e453ab347e57742141ad3016b63223fe8fc237ee8e/Glass.002.jpeg" />So the two states exist in superposition, until we reach an edge, where typically one particular orientation is favoured. This represents a measurement in quantum mechanics: the collapse of the wave function. * The Consistent Histories Interpretation, proposed by R.B. Griffiths (1984) and elucidated by the late Pierre Hohenberg in his Reviews of Modern Physics article (2009).** This statement is shared by all interpretations of quantum mechanics. https://eeedg.ca/page-4 Thu, 11 Aug 2022 03:04:23 +0000 eeedg https://eeedg.ca/page-4 The degree to which this effect is present varies from piece to piece. Those with the Ziggurat feature look highly coherent and therefore highly entangled, in the quantum interpretation. Those with Waves show structure at the larger scales, representing the classical domain where indeed what we typically measure are waves. <img width="559" height="684" width_o="559" height_o="684" data-src="https://freight.cargo.site/t/original/i/eb974b5865c2ec5fe2806e099670aa084aa39537136f2cfe1a5ffd749eaf5e30/172000060_crop.jpg" data-mid="150130229" border="0" src="https://freight.cargo.site/w/559/i/eb974b5865c2ec5fe2806e099670aa084aa39537136f2cfe1a5ffd749eaf5e30/172000060_crop.jpg" /> <img width="1920" height="2400" width_o="1920" height_o="2400" data-src="https://freight.cargo.site/t/original/i/645437fe4e7ef3292e23f7339273031633b77334a17186eeace8b1ceec025a4a/172000060.jpg" data-mid="150130230" border="0" src="https://freight.cargo.site/w/1000/i/645437fe4e7ef3292e23f7339273031633b77334a17186eeace8b1ceec025a4a/172000060.jpg" /> ( These effects can coexist, as here ) In contrast, those without any Shadow and without Flow are typically the most ambiguous. <img width="1920" height="2400" width_o="1920" height_o="2400" data-src="https://freight.cargo.site/t/original/i/e7acddb3f46d049435c2acc53b78aa6f8c3dc0ceffa1588ec2b3a7cb624fad02/344000001.jpg" data-mid="150130501" border="0" src="https://freight.cargo.site/w/1000/i/e7acddb3f46d049435c2acc53b78aa6f8c3dc0ceffa1588ec2b3a7cb624fad02/344000001.jpg" /> <img width="882" height="1104" width_o="882" height_o="1104" data-src="https://freight.cargo.site/t/original/i/1854920a0538af61ef4d578514adec1556087be7b550de9a7ae21ff3a7bf9540/344000001_crop.jpg" data-mid="150130523" border="0" src="https://freight.cargo.site/w/882/i/1854920a0538af61ef4d578514adec1556087be7b550de9a7ae21ff3a7bf9540/344000001_crop.jpg" /> https://eeedg.ca/page-5 Thu, 11 Aug 2022 01:44:02 +0000 eeedg https://eeedg.ca/page-5 Yet when we zoom out, we can appreciate a harmonious whole. This represents the classical world to which we are accustomed. Its apparent solidity depends on our not looking too closely. <img width="669" height="801" width_o="669" height_o="801" data-src="https://freight.cargo.site/t/original/i/359552a762af1ab7e386e4c1b11da80d64461df0a076b18609aef61c17bc6021/crop.jpg" data-mid="150125744" border="0" src="https://freight.cargo.site/w/669/i/359552a762af1ab7e386e4c1b11da80d64461df0a076b18609aef61c17bc6021/crop.jpg" /> <img width="882" height="1104" width_o="882" height_o="1104" data-src="https://freight.cargo.site/t/original/i/faee7ed518253371a852e12bff4479a74e9048f5ead6e241214334f6e9e9ff04/344000001_crop.jpg" data-mid="150125800" border="0" src="https://freight.cargo.site/w/882/i/faee7ed518253371a852e12bff4479a74e9048f5ead6e241214334f6e9e9ff04/344000001_crop.jpg" /> <img width="1024" height="1304" width_o="1024" height_o="1304" data-src="https://freight.cargo.site/t/original/i/903241a7c904c95fdac188abe67097ad272920c0f244fbe5f62ac7964a2af930/344000007_crop.jpg" data-mid="150125803" border="0" src="https://freight.cargo.site/w/1000/i/903241a7c904c95fdac188abe67097ad272920c0f244fbe5f62ac7964a2af930/344000007_crop.jpg" /> https://eeedg.ca/page-6 Thu, 11 Aug 2022 01:55:31 +0000 eeedg https://eeedg.ca/page-6 Each piece from Glass represents a composite, uncertain reality.&nbsp;&nbsp;&nbsp; <img width="939" height="1148" width_o="939" height_o="1148" data-src="https://freight.cargo.site/t/original/i/4094afa49afe054ccabcfab8b5cea395ec21b255782b09a5ab2e9f93421006fa/172000038_crop.jpg" data-mid="150164290" border="0" src="https://freight.cargo.site/w/939/i/4094afa49afe054ccabcfab8b5cea395ec21b255782b09a5ab2e9f93421006fa/172000038_crop.jpg" /> Every experience is highly personal. The path that you trace will generally not be the same as that taken by anyone else in the same circumstances. Moreover, a definite path only comes into existence through your experience. This is also a fact of quantum mechanics (#). As Heisenberg said, ‘Die "Bahn" entsteht erst dadurch, dass wir sie beobachten.' ( The trajectory only comes into existence by us observing it. )Glass was released as a series of 300 on Artblocks on August 22, 2022.&nbsp; View Glass at Artblocks |&nbsp;Archipelago | Opensea It is written in javascript, using the p5.js library. The code necessary to reproduce each piece is preserved indefinitely on the Ethereum blockchain. Glass is part of a larger attempt to intuitively communicate ideas at the leading edge of theoretical physics. My general research interest is the emergence of complexity in the world. Previous generative art series have looked at the emergence of complexity in language (Alien Tongues, Alien Codex) and life as a state of matter (Spectral Beings), which are the two current directions of my professional research program. (#) If you’re curious about how Glass can be mapped more quantitatively to quantum mechanics, imagine that the orientation of the panes is like the direction of an electron’s spin, either vertical or horizontal (In reality spins would usually be up or down, but this is immaterial to the discussion.). In isolation, a cluster of spins could point in either orientation; the states exist in superposition. Measurement causes the states to locally collapse to a definite spin. But observers coming from elsewhere might measure a different orientation, and these histories might not agree. &nbsp; https://eeedg.ca/Emergence Tue, 29 Mar 2022 03:16:05 +0000 eeedg https://eeedg.ca/Emergence Emergence: on the potential of long-form generative art Generative art is not new. Since at least the 1950's, pioneering artists have used computers, plotters, and other machines to make artwork in which partial control was handed over to a mechanical intermediary. Generative art extends the human use of machine from technical tool to artistic medium. <img width="512" height="600" width_o="512" height_o="600" data-src="https://freight.cargo.site/t/original/i/4198e6d6d8f7ce6376b8514637f06a028e0a81eb1a483e054fe1a3aceac43224/franke-3_o.jpeg" data-mid="137867031" border="0" data-scale="86" src="https://freight.cargo.site/w/512/i/4198e6d6d8f7ce6376b8514637f06a028e0a81eb1a483e054fe1a3aceac43224/franke-3_o.jpeg" /> Analog-Grafik D3 (Dance of the Electrons) Herbert Franke, 1960. <img width="1073" height="1080" width_o="1073" height_o="1080" data-src="https://freight.cargo.site/t/original/i/3fde05e20757a8f77658c08f688ee7bdea4ed0cf372977ba1df5a91ea7a02fbd/1969-70_Mohr_P-021-BandStructure.jpeg" data-mid="137867029" border="0" src="https://freight.cargo.site/w/1000/i/3fde05e20757a8f77658c08f688ee7bdea4ed0cf372977ba1df5a91ea7a02fbd/1969-70_Mohr_P-021-BandStructure.jpeg" />P-021-Band Structure Manfred Mohr, 1969. The medium has always taken advantage of new technologies as they appear. A recent development is what Tyler Hobbs coined as `long-form’ generative art: a version of the latter in which a code is used to produce a series of outputs, typically 100-1000, where the seed specifying a particular output is chosen randomly at the moment of creation. NFT architecture beautifully facilitates long-form generative art, as evidenced by the success of the Artblocks platform. When a user mints a piece from a long-form set, their participation creates the spark that brings their particular mint to life. <img width="890" height="1070" width_o="890" height_o="1070" data-src="https://freight.cargo.site/t/original/i/0231d988a79f0050f58cc2cc59118e2153d7c5d77770ed1d5c7da6a0e2496aff/Fidenza946.jpg" data-mid="137867023" border="0" src="https://freight.cargo.site/w/890/i/0231d988a79f0050f58cc2cc59118e2153d7c5d77770ed1d5c7da6a0e2496aff/Fidenza946.jpg" /> <img width="890" height="1072" width_o="890" height_o="1072" data-src="https://freight.cargo.site/t/original/i/a66fd0477fd4b82acf6ab85a7473186ea5d941d162dc1becf0a55d75d34f4e4b/Fidenza917.jpg" data-mid="137867021" border="0" src="https://freight.cargo.site/w/890/i/a66fd0477fd4b82acf6ab85a7473186ea5d941d162dc1becf0a55d75d34f4e4b/Fidenza917.jpg" /> <img width="889" height="1077" width_o="889" height_o="1077" data-src="https://freight.cargo.site/t/original/i/81c7336f3798aab7e2c0f20a75e9638a83e182ce441a90aab3e1feb0e00a466a/Fidenza873.jpg" data-mid="137867020" border="0" src="https://freight.cargo.site/w/889/i/81c7336f3798aab7e2c0f20a75e9638a83e182ce441a90aab3e1feb0e00a466a/Fidenza873.jpg" /> <img width="888" height="1070" width_o="888" height_o="1070" data-src="https://freight.cargo.site/t/original/i/9006d808b998f23309a8b55d58e224d5c6b678ef4a14300c9b8470afc6b795ea/Fidenza745.jpg" data-mid="137867019" border="0" src="https://freight.cargo.site/w/888/i/9006d808b998f23309a8b55d58e224d5c6b678ef4a14300c9b8470afc6b795ea/Fidenza745.jpg" /> Fidenza, Tyler Hobbs, 2021. In his essay, Tyler discussed the acute challenges of long-form. Instead here I want to focus on its potential, and how this potential mirrors some of the thorniest questions faced by contemporary scientists (*). Since a long-form system must generate a large series of outputs, to maintain interest it must engender processes that create variety. The latter can be tightly controlled: for example, the system may choose between a set of palettes, and a series of brush sizes, but otherwise use the same hyperparameters to control the structure and rendering of artistic elements. Many long-form systems do exactly this. This strategy allows the artist to create a highly cohesive series, and aids in quality control. However, the potential is much greater and, in my view, profound. For a long-form system can create emergent structures that were not imagined whatsoever by the artist. Emergence -- loosely speaking the phenomenon in which the whole is more than the sum of the parts-- is at the heart of many of nature's mysteries. How does life emerge from chemical reactions? How does consciousness emerge from the firing of millions of neurons? It is also present in some of the most celebrated long-form systems. Dmitri Cherniak's Ringers, which takes classic design elements and elevates them to a long-form system, features a large number of legible anthropomorphic forms, none of which were hard-coded in. Among these, the Goose is famous, and in my opinion justifiably so. <img width="1066" height="1066" width_o="1066" height_o="1066" data-src="https://freight.cargo.site/t/original/i/26b43a9b10ce0075ea78cc52672a0161c6013476153bd78a58f231ffe5750f44/Ringer984.jpg" data-mid="137867014" border="0" src="https://freight.cargo.site/w/1000/i/26b43a9b10ce0075ea78cc52672a0161c6013476153bd78a58f231ffe5750f44/Ringer984.jpg" /> <img width="1200" height="1200" width_o="1200" height_o="1200" data-src="https://freight.cargo.site/t/original/i/e448e42f2edf0ce534386c24fc45d604d34508cfa9a0be682571b8bedf0b1478/Goose.jpeg" data-mid="137867017" border="0" src="https://freight.cargo.site/w/1000/i/e448e42f2edf0ce534386c24fc45d604d34508cfa9a0be682571b8bedf0b1478/Goose.jpeg" /> The Goose <img width="1066" height="1068" width_o="1066" height_o="1068" data-src="https://freight.cargo.site/t/original/i/0f67139a8891f4a15e62843ab5ae965de9830778e9d701315207c816c33688e5/Ringer917.jpg" data-mid="137867015" border="0" src="https://freight.cargo.site/w/1000/i/0f67139a8891f4a15e62843ab5ae965de9830778e9d701315207c816c33688e5/Ringer917.jpg" /> <img width="1066" height="1066" width_o="1066" height_o="1066" data-src="https://freight.cargo.site/t/original/i/b93e8c776585d3ae5f53ed90d498606dcc09a8e285fda737be8939d22cb5f2f7/Ringer971.jpg" data-mid="137867016" border="0" src="https://freight.cargo.site/w/1000/i/b93e8c776585d3ae5f53ed90d498606dcc09a8e285fda737be8939d22cb5f2f7/Ringer971.jpg" /> Ringers, Dmitri Cherniak, 2021. The key point is this: if a long-form system is rich enough to create emergent structures, then its output space must be large and may effectively be infinite. It is practically impossible for the artist to control all the variety inherent in their system. One cannot have the Goose Ringer without all the non-geese. So a system that generates emergent variety must necessarily embrace fluctuations in a manner beyond those that generate only tightly controlled variety. This potential for emergence is absent from earlier forms of generative art, and among all artistic media may be unique to long-form generative art. The vast combinatorial spaces explored by long-form generative art mirror those explored effortlessly by nature. The origin of life is a difficult problem because we have little idea how big of a space nature has explored -- we don’t know how lucky we are, and we cannot effectively do experiments to `generate’ an origin of life in other corners of chemical space. Understanding how systems of massive variety can nevertheless share universal features is a core component of my research program in physics.In the world of generative art, emergent variety is clearly valued by collectors, who speak of `transcendent grails’. The potential to mint such a piece adds urgency and tension to the process, beyond simply gambling for controlled rarity: a collector might, in a real sense, mint a piece that would never otherwise have existed in the universe. <img width="1784" height="1784" width_o="1784" height_o="1784" data-src="https://freight.cargo.site/t/original/i/1f4612f67aa01a53ce5f5c2879efe2c43d53a08c421b05156ffd66214b38dde4/000_Stitched_oopTAGSaj5yzfzC3LMqW9u8GRSVnwEkD4ioHtD4rWDsGKEF97BB.jpg" data-mid="138472866" border="0" src="https://freight.cargo.site/w/1000/i/1f4612f67aa01a53ce5f5c2879efe2c43d53a08c421b05156ffd66214b38dde4/000_Stitched_oopTAGSaj5yzfzC3LMqW9u8GRSVnwEkD4ioHtD4rWDsGKEF97BB.jpg" /> <img width="1784" height="1784" width_o="1784" height_o="1784" data-src="https://freight.cargo.site/t/original/i/374bef8d54eafb5ef6eefa9b77064122cf39bf2ae32a87afad7035352886008b/010_Stitched_ooK5TtMiECeoT8GE7WBWq3X7Y5JocP4VHb1ZUjzVCGPPTY719Ji.jpg" data-mid="138472872" border="0" src="https://freight.cargo.site/w/1000/i/374bef8d54eafb5ef6eefa9b77064122cf39bf2ae32a87afad7035352886008b/010_Stitched_ooK5TtMiECeoT8GE7WBWq3X7Y5JocP4VHb1ZUjzVCGPPTY719Ji.jpg" /> <img width="1784" height="1784" width_o="1784" height_o="1784" data-src="https://freight.cargo.site/t/original/i/54e75a67281d0681946a2fc8623a014d76a170bd97b8eb10dca963c5f10e3b3f/003_Stitched_opRAmRcBQVPy9upeFPke5xUHn1n2o1W26hSNC2XQxP8QEFr8Ty1.jpg" data-mid="138472873" border="0" src="https://freight.cargo.site/w/1000/i/54e75a67281d0681946a2fc8623a014d76a170bd97b8eb10dca963c5f10e3b3f/003_Stitched_opRAmRcBQVPy9upeFPke5xUHn1n2o1W26hSNC2XQxP8QEFr8Ty1.jpg" /> <img width="1784" height="1784" width_o="1784" height_o="1784" data-src="https://freight.cargo.site/t/original/i/6972da403f496fbe9d09d919f3bf10239db3649e2a1a90a30fd70ff843f0d559/034_Stitched_ooMZZZTAUdUTHU95qETAm5tFKiiAy5P9Txb8YeWxXmhtaRG8ziL.jpg" data-mid="138472871" border="0" src="https://freight.cargo.site/w/1000/i/6972da403f496fbe9d09d919f3bf10239db3649e2a1a90a30fd70ff843f0d559/034_Stitched_ooMZZZTAUdUTHU95qETAm5tFKiiAy5P9Txb8YeWxXmhtaRG8ziL.jpg" /> Stitched, pepe xyz (EDG), 2022 As an artist I experimented with these themes in my series Stitched and its accompaniment Stitched: Trauma. In the former, I honed in on a clear vision and allowed controlled variety around it. In Trauma, instead I allowed a certain amount of wildness. The resulting series is harder to pin down, but led to many unexpected outputs. <img width="2082" height="2082" width_o="2082" height_o="2082" data-src="https://freight.cargo.site/t/original/i/136cfec5eb7375e1eed822592079af93714bc253f5f18574d268e03884a7cc79/001_Stitched_Trauma_ooRDUeQbp4MAcZ8kobXbhh4Zmyka7Z14n1tAkhWdbtie3zAY6eh.jpg" data-mid="138472870" border="0" src="https://freight.cargo.site/w/1000/i/136cfec5eb7375e1eed822592079af93714bc253f5f18574d268e03884a7cc79/001_Stitched_Trauma_ooRDUeQbp4MAcZ8kobXbhh4Zmyka7Z14n1tAkhWdbtie3zAY6eh.jpg" /> <img width="1694" height="1694" width_o="1694" height_o="1694" data-src="https://freight.cargo.site/t/original/i/d392752758a096f7678cc4395651eb5f9e42a85fcc1cbdbb0c55b02066b51276/322_Stitched_Trauma_op7GbFcyvLXYStsiiLhiSz4BC1mTdkUZRxCFCiooC64mdYEAtqT.jpg" data-mid="138472959" border="0" src="https://freight.cargo.site/w/1000/i/d392752758a096f7678cc4395651eb5f9e42a85fcc1cbdbb0c55b02066b51276/322_Stitched_Trauma_op7GbFcyvLXYStsiiLhiSz4BC1mTdkUZRxCFCiooC64mdYEAtqT.jpg" /> <img width="1808" height="1808" width_o="1808" height_o="1808" data-src="https://freight.cargo.site/t/original/i/79446aafd452c70118b86d85628ede21b949220b77c119a05db0b6d8e7897166/310_Stitched_Trauma_oozpCToiak8UmmQZgMRLh3PsaNEe2WGje7QLVJWJGPPwLkPhSej.jpg" data-mid="138472867" border="0" src="https://freight.cargo.site/w/1000/i/79446aafd452c70118b86d85628ede21b949220b77c119a05db0b6d8e7897166/310_Stitched_Trauma_oozpCToiak8UmmQZgMRLh3PsaNEe2WGje7QLVJWJGPPwLkPhSej.jpg" /> <img width="1828" height="1828" width_o="1828" height_o="1828" data-src="https://freight.cargo.site/t/original/i/c93c867b5a78b52454be2ec7ee0ccaab7c9a3b88d71e9521053325ade3004dd4/449_Stitched_Trauma_onyvBLQocdTUR1X2wbdjhVD2H7aH8VZaVuXLMPsasLhZV84rHhK.jpg" data-mid="138472958" border="0" src="https://freight.cargo.site/w/1000/i/c93c867b5a78b52454be2ec7ee0ccaab7c9a3b88d71e9521053325ade3004dd4/449_Stitched_Trauma_onyvBLQocdTUR1X2wbdjhVD2H7aH8VZaVuXLMPsasLhZV84rHhK.jpg" />Stitched: Trauma,pepe xyz (EDG), 2022 We are only scratching the surface of what emergent forms might be possible to create with generative art.&nbsp; In my series, Mazinaw, I embrace variety; the code has been designed to produce an infinite number of emergent structures.&nbsp; <img width="2880" height="2304" width_o="2880" height_o="2304" data-src="https://freight.cargo.site/t/original/i/ed14d3fc32d3ab3039da021d537b3ccc95921ef3cc7e0cce98c4780c584c3381/Mazinaw_22.jpg" data-mid="137869279" border="0" src="https://freight.cargo.site/w/1000/i/ed14d3fc32d3ab3039da021d537b3ccc95921ef3cc7e0cce98c4780c584c3381/Mazinaw_22.jpg" /> <img width="2880" height="2304" width_o="2880" height_o="2304" data-src="https://freight.cargo.site/t/original/i/efdeec6a221690d03cc3d42b39da173a3179aab1406003c3cba5d98879f55308/Mazinaw_86.jpg" data-mid="137869276" border="0" src="https://freight.cargo.site/w/1000/i/efdeec6a221690d03cc3d42b39da173a3179aab1406003c3cba5d98879f55308/Mazinaw_86.jpg" /> <img width="2880" height="2304" width_o="2880" height_o="2304" data-src="https://freight.cargo.site/t/original/i/3b6061e43bedd486e91ca4a5999e054f178d2f65ba8c44abdc513f80399c4507/Mazinaw_42.jpg" data-mid="137869278" border="0" src="https://freight.cargo.site/w/1000/i/3b6061e43bedd486e91ca4a5999e054f178d2f65ba8c44abdc513f80399c4507/Mazinaw_42.jpg" /> <img width="2880" height="2304" width_o="2880" height_o="2304" data-src="https://freight.cargo.site/t/original/i/835377add8ccea27a4d2d7a0aef4ae245d36e4f77aa5167a66ccb18d8cbcda0e/Mazinaw_77.jpg" data-mid="137869277" border="0" src="https://freight.cargo.site/w/1000/i/835377add8ccea27a4d2d7a0aef4ae245d36e4f77aa5167a66ccb18d8cbcda0e/Mazinaw_77.jpg" /> Mazinaw [testnet]&nbsp; EDG, 2022 But only 256 of them will ever exist. Mazinaw can be seen on the Artblocks platform. It is meant to be viewed in full screen, or printed. EDG 2022 [ home ] (*) The author is a practicing theoretical physicist. https://eeedg.ca/1-copy Wed, 15 Dec 2021 05:13:43 +0000 eeedg https://eeedg.ca/1-copy Spectral Beings: Morphogenesis Spectral Beings are a series of 888 generative art works, rendered in javascript with the p5.js library, originally released on September 24, 2021. The 11kb code needed to create them is stored indefinitely on the ethereum blockchain.&nbsp;The series is inspired by the uncomfortable thought that aliens are likely out there in the universe, but, by virtue of the great distances involved, utterly inaccessible to us. This dilemma presents an opportunity: to imagine an alien biology, following general principles that we establish on Earth.In my day job as a theoretical physicist I work on the theory of living matter, using the fundamental laws of physics as constraints. But by night, I can take these same constraints and, through generative art, imagine the endless possibilities afforded by them.Spectral beings explores the possibility of life made from light itself. The beings take a variety of forms.. <img width="1024" height="1024" width_o="1024" height_o="1024" data-src="https://freight.cargo.site/t/original/i/9d442b8e750a2cc51733fc4f4ec38ec8cc585352e77431deb814db4fb83d3b94/SB_thumb_160..png" data-mid="127441925" border="0" src="https://freight.cargo.site/w/1000/i/9d442b8e750a2cc51733fc4f4ec38ec8cc585352e77431deb814db4fb83d3b94/SB_thumb_160..png" /> <img width="1024" height="1024" width_o="1024" height_o="1024" data-src="https://freight.cargo.site/t/original/i/f4c74aa705db6c54f722dbb546555485d4d2ca65a21e7ce5f277965b06f23d22/SB_thumb_111.-1.png" data-mid="127442180" border="0" src="https://freight.cargo.site/w/1000/i/f4c74aa705db6c54f722dbb546555485d4d2ca65a21e7ce5f277965b06f23d22/SB_thumb_111.-1.png" /> <img width="1024" height="1024" width_o="1024" height_o="1024" data-src="https://freight.cargo.site/t/original/i/a81f2a23752c4147dff95c330aeb933479cacea305af9662ee96af978bd36532/SB_thumb_196..png" data-mid="127442441" border="0" src="https://freight.cargo.site/w/1000/i/a81f2a23752c4147dff95c330aeb933479cacea305af9662ee96af978bd36532/SB_thumb_196..png" /> <img width="1024" height="1024" width_o="1024" height_o="1024" data-src="https://freight.cargo.site/t/original/i/de7e02f34f40cc6f7ecdd7e27d7e2a09086878574a07ac284914abc52ba3d3ec/SB_thumb_129..png" data-mid="127442106" border="0" src="https://freight.cargo.site/w/1000/i/de7e02f34f40cc6f7ecdd7e27d7e2a09086878574a07ac284914abc52ba3d3ec/SB_thumb_129..png" /><img width="1024" height="1024" width_o="1024" height_o="1024" data-src="https://freight.cargo.site/t/original/i/3c147a609ac0639a6d08aa86c25c086ffd8a615c7d0ae7b445f92221f92158f9/SB_thumb_181..png" data-mid="127442439" border="0" src="https://freight.cargo.site/w/1000/i/3c147a609ac0639a6d08aa86c25c086ffd8a615c7d0ae7b445f92221f92158f9/SB_thumb_181..png" /> <img width="1024" height="1024" width_o="1024" height_o="1024" data-src="https://freight.cargo.site/t/original/i/aeb0575b20fbafaaaf6ec7fa873968330a31ba1df7e07e0f3e831c1843f56865/SB_thumb_238..png" data-mid="127442446" border="0" src="https://freight.cargo.site/w/1000/i/aeb0575b20fbafaaaf6ec7fa873968330a31ba1df7e07e0f3e831c1843f56865/SB_thumb_238..png" /> <img width="1024" height="1024" width_o="1024" height_o="1024" data-src="https://freight.cargo.site/t/original/i/cbb9aaf6a2321f8a0a3f7c1a5b6f4be98309715b336b8f22cf97b598ab671444/SB_thumb_85..png" data-mid="127442123" border="0" src="https://freight.cargo.site/w/1000/i/cbb9aaf6a2321f8a0a3f7c1a5b6f4be98309715b336b8f22cf97b598ab671444/SB_thumb_85..png" /><img width="1024" height="1024" width_o="1024" height_o="1024" data-src="https://freight.cargo.site/t/original/i/a1015d25389ee3c9655041af9823f539a1ddea44520316e50fe023ff9230ff53/SB_thumb_78..png" data-mid="127442184" border="0" src="https://freight.cargo.site/w/1000/i/a1015d25389ee3c9655041af9823f539a1ddea44520316e50fe023ff9230ff53/SB_thumb_78..png" /><img width="1024" height="1024" width_o="1024" height_o="1024" data-src="https://freight.cargo.site/t/original/i/fbaa9db7b8060bdbc2b85aba033bbc4cce72bd6389835f47720b15661cc1e37a/SB_thumb_197..png" data-mid="127442445" border="0" src="https://freight.cargo.site/w/1000/i/fbaa9db7b8060bdbc2b85aba033bbc4cce72bd6389835f47720b15661cc1e37a/SB_thumb_197..png" /> [ from top, left to right: #160, #129, #85, #111, #181, #78, #196, #238, #197 ] ..but are all created from the same short code. [ the originals are fully periodic 4s films. clicking on an image above will take you to the corresponding film. ] Each spectral being is uniquely specified by its seed value, generated on mint. This seed is a compressed key, inscrutable to the human eye but readable by the code itself. Much as our bodies use DNA to generate a suite of proteins, which carry functional significance, the seed value is parsed by the code to generate parameter values, which control the shape of each being. This article sketches this imagined alien genetic code. In the accompanying Appendix, I explain in more mathematical detail a key technique used in Spectral Beings, which should be of general interest for generative artists. Each Spectral Being begins as a templated body form, with a number of antenna and body `lobes’. The details specifying this form are random and controlled by the seed. For example, the antenna angle, number of segments, relative head size, etc., are all variable. Here are some examples. alpha controls the relative head size, while each half-lobe is numbered. <img width="728" height="727" width_o="728" height_o="727" data-src="https://freight.cargo.site/t/original/i/2d0c7ff0e0ce764848b5294390f3ded9550dc35c6d2f1188a696867cf29e0140/SB_gro_thumb_129.-Plan.png" data-mid="141805227" border="0" data-scale="59" src="https://freight.cargo.site/w/728/i/2d0c7ff0e0ce764848b5294390f3ded9550dc35c6d2f1188a696867cf29e0140/SB_gro_thumb_129.-Plan.png" /> <img width="725" height="725" width_o="725" height_o="725" data-src="https://freight.cargo.site/t/original/i/9b9a4fb724e9ba80ffc0a019e579e322f1b3563928e78c82d8ab4c3c387cd5e8/SB_gro_thumb_160.plan.png" data-mid="141805224" border="0" data-scale="60" src="https://freight.cargo.site/w/725/i/9b9a4fb724e9ba80ffc0a019e579e322f1b3563928e78c82d8ab4c3c387cd5e8/SB_gro_thumb_160.plan.png" /> Although this already allows for a great variety of forms, the bodies are still just templates, with a roughly cylindrical shape. The beings are three dimensional, and at this point you can imagine a vertical y axis, and at each y, some radius r(y). Create a circle of that radius, and you’ll build up a hollow three dimensional form. Let’s fix the y axis to go from 0 to 100. Then, as we go from 0 to 100, the shape of the being is specified by r(0), r(1), and so on, up to r(100). (In reality, they are not perfectly symmetrical, but let’s ignore this complication)The next, crucial, step is a form of domain distortion. The key idea is simple: instead of plotting a point at y and r(y), we can pass the vertical and radial coordinates through functions f and g, and create a circle at f(y) with radius g(r(y)). If that sounds abstract, consider the following figure. The left side shows a templated form, with some segments marked out by green curves. Under the functions f and g, these curves get transformed, into the curves shown on the right side. The simplest class of domain distortion stretches or shrinks segments, but does not fold over shapes onto themselves. In this case the initial template is legible in the final body forms, but clearly the latter have character going much beyond their morphogenetic precursor. <img width="1459" height="724" width_o="1459" height_o="724" data-src="https://freight.cargo.site/t/original/i/0d590a5cb086f9fde270143d34066f0f04ef5375baa64c3fd5b88cd4d7052b8e/SB_gro_thumb_160..png" data-mid="141805225" border="0" src="https://freight.cargo.site/w/1000/i/0d590a5cb086f9fde270143d34066f0f04ef5375baa64c3fd5b88cd4d7052b8e/SB_gro_thumb_160..png" /> <img width="1464" height="728" width_o="1464" height_o="728" data-src="https://freight.cargo.site/t/original/i/949da844d4fc43633fb8a7ea1f7299deae31f95d3f9a260cb01992eb89f4d5f1/SB_gro_thumb_129..png" data-mid="141805226" border="0" src="https://freight.cargo.site/w/1000/i/949da844d4fc43633fb8a7ea1f7299deae31f95d3f9a260cb01992eb89f4d5f1/SB_gro_thumb_129..png" /> By varying the domain distortion functions, a huge variety of forms can be created. For example, suppose we map a body segment so that the ‘waist’ touches the ‘knee’. Then we get a ballerina:<img width="1462" height="727" width_o="1462" height_o="727" data-src="https://freight.cargo.site/t/original/i/94bc482629fd00d846c787650e6c24b50e1b38b7572a8c564edce021712a419a/SB_gro_thumb_78..png" data-mid="141805230" border="0" data-scale="50" src="https://freight.cargo.site/w/1000/i/94bc482629fd00d846c787650e6c24b50e1b38b7572a8c564edce021712a419a/SB_gro_thumb_78..png" />More intricate forms can be created by folding over body parts onto themselves. We can take what was the head, and map it onto the body core. Then the final form will have multiple ‘organs’, as in Spectral Beings 111 (left) or 160 (right): <img width="1461" height="720" width_o="1461" height_o="720" data-src="https://freight.cargo.site/t/original/i/a52558d047022907555b9cb64e8ab6bf03a5006c41ef6fb53a07d350c3b72f8d/SB_gro_thumb_111..png" data-mid="141805228" border="0" data-scale="100" src="https://freight.cargo.site/w/1000/i/a52558d047022907555b9cb64e8ab6bf03a5006c41ef6fb53a07d350c3b72f8d/SB_gro_thumb_111..png" /> <img width="1462" height="723" width_o="1462" height_o="723" data-src="https://freight.cargo.site/t/original/i/114649e7b6ed4f6da7b2cd1d865c093095e1c82372b4a11f167aea9f791d641a/SB_gro_thumb_85..png" data-mid="141805229" border="0" src="https://freight.cargo.site/w/1000/i/114649e7b6ed4f6da7b2cd1d865c093095e1c82372b4a11f167aea9f791d641a/SB_gro_thumb_85..png" /> These examples only scrape the surface of what is possible. Perusing the full series you will see many more.Similar forms of domain distortion are used by extant life in morphogenesis. For example, overexpression of a protein in the middle of the cell can cause a pinch -- one type of distortion -- that leads to cell division. Other expression patterns can lead to bulges, folds, stripes, appendages, and so on. Of course, while life in reality needs to follow the laws of physics, each morphogenetic phenomenon having a microscopic basis in chemical reactions, with generative art we can free ourselves of these limitations. Spectral Beings uses a large family of distortion functions chosen for their aesthetic consequences.&nbsp; Domain distortion is a general tool, useful in many contexts. In milder forms, it can add nuance and variety to simple shapes, while in more extreme versions, it offers endless possibilities for morphogenesis, limited only by the creativity of the artist. &nbsp;Appendix Here we explain domain distortion in more mathematical terms. For simplicity, consider the one dimensional case. We write y for the initial coordinate, and Y for the transformed one. Y = f(y) where f is the domain distortion function. How does the form of f control the resulting shape? Consider first the trivial case f(y) = y. Then Y=y and there is no distortion at all. Now let us add complexity. f(y) = c y, where c is some constant, just scales y by a constant factor c. f(y) = y + a, where a is some constant, shifts y by a constant factor a. We can, of course, combine these: f(y) = c y + a performs both a shift and a scaling. But these examples are hardly deserving of the name distortion. To go further, we need to consider nonlinear functions f.&nbsp; An endless family of functions are possible. In Spectral Beings, the domain distortion functions are chosen from trigonometric functions, like the sine function. To understand why this family is interesting, consider what happens when f(y) has a local maximum, say at y*. Let f(y*) = Y*. Then for y a little bit smaller than y*, we have f(y) &lt; Y. And similarly for y a little bit larger than y*, we also have f(y) &lt; Y. Close enough to y*, for each point y1 we can find another point y2 on the other side of y* that maps to the same value Y1. Thus this distortion creates a fold. A similar argument applies to local minima, which also create folds. With the trigonometric functions, we can create a variable number of folds, just by controlling n in the expression f(y) = sin(n y). If y goes from 0 to 2 Pi, then when n=1 we get one local maximum and one local minimum: two folds. But if n=2, then we get 4 folds. And so on. Moreover, we can also add a phase to the function: f(y) = sin(n y + b). By varying b, we control where the folds occur. Do they start at the head, or somewhere further down?&nbsp; Again, all these complexities can be combined. In Spectral Beings, both the vertical coordinates y and the radial coordinates r are distorted. The resulting functions are much harder to visualize, although the same mathematical principles apply.&nbsp;