Automatic, Spontaneous Things

A tribute to the cryptoart of hex6c

Takens Theorem
8 min readAug 11, 2021

Blockchain is an alluring synthesis of the automatic and the spontaneous, the machine and the human. Blockchain permits automation of many economic activities. But behind these automations are the complex intentions of human agents. Perhaps more than anywhere else, it is cryptoart where this marriage of ideas is most complete. Ownership of a work of art is encoded on chain, cold and crisp, marking provenance with permanence. But enthusiasm about cryptoart derives from human creativity — an alluring product of a spontaneous, creative mind. That creativity, once encapsulated in digital form, is secured forever, giving its holder pride of ownership and appreciation.

This makes blockchain a viable subject for creative framing and analysis. Some powerful cryptoart depicts the underlying ethos and ideas of blockchain. A Josie Bellini piece, for example, strikes the viewer with an austere juxtaposition of humans, human society and the expected impact that blockchain will have. Her Tune In #5 illustrates this starkly — a human form becoming embedded in the digital, preparing herself for projection into new, future virtual worlds. Similar conceptual elaborations come from the amazing minds of cryptograffiti, Coldie, Nelly and others.

But blockchain — the technical foundation itself — may be the subject of this creative exploration too. The algorithmic form and resulting data of the blockchain are alluring in their own right. The blockchain offers enticing hints of the future, but it also contains permanent echoes of its past. A blockchain is at once historical and futuristic. This property gives it a conceptual profundity of very few digital things, especially because its digital traces — stored automatically forever — contain echoes of that human dimension noted above.

The work of hex6c embodies this approach to cryptoart. Since 2018, hex6c has been creating beautiful renderings by manipulating data and algorithmic form inspired by blockchain and related computational concepts. The result is often mysterious and awe-inspiring. Consider, for example, “Ethereum Genesis Block,” the featured image of the present article. This is a “coilgram” from 2018. hex6c uses the hash from a block (here, Ethereum’s genesis block) and unwinds a deterministic coil, with shape and color computed from this hash.

hex6c’s works often go beneath their blockchain inspiration, echoing digital creativity and computational origins of the past. For example, the coilgram algorithm is partly derived from so-called “Perlin noise,” named for a computer scientist whose work famously impacted early animation, in particular Tron (1982). Again we see this synthesis of the automated and the human, the blockchain and its past, new innovative cryptoart with tributes of its own. hex6c combines the technical elements of crypto with elements of other realms into elaborate digital representations of Turing completeness, cryptography and prime numbers and more.

These traits of hex6c’s work are, in some ways, predictable from his other work. He is a scholar, a mathematician and a curator himself. In a wide ranging collaboration, including with other artists like Hackatao and MLOdotArt, they put forward a kind of cryptoart thesis in 2018. The thesis is didactic too — explaining the many technical ingredients of emerging cryptoart over 2 years ago. hex6c even proposed quantitative curatorial tools that cryptoart makes possible.

hex6c has supported the cryptoart landscape with his many skills over several years — as a mathematician, as a curator, and also as an artist. This brief blog post is a tribute to this artist. I draw on a beautiful paradox of his work. It contains these elements of automated precision, yet reflects spontaneous human creativity — automatic, spontaneous, alluring things.

Seven pieces are illustrated below. In communicating directly with hex6c, some of his favorite pieces are here combined with my own.

1. Ethereum Genesis Block, SuperRare, 2018

Ethereum Genesis Block, SuperRare, 2018

A creative representation of the Ethereum Genesis Block. This is part of the Coilgram series that tells the history of blockchains through these coiled representations of iconic moments (identified by blocks) of several blockchains. Coilgram is an algorithm that reads a block hash and uses it to forge artworks shaped as colored intertwined coils. The method is deterministic: the same hash as input gives the same coiled design as output. Moreover, different hashes generate different coils (in shape and color).

This is also a tribute to the work of Perlin, whose algorithm motivates the Coilgram series and was foundational to early animation.

2. “Game of Pixel” method from 2018

Invasion 68” with the “Game of Pixel” method

In 2018, hex6c devised a brilliant “Game of Pixel,” adapting mathematician Conway’s famous “Game of Life”. Conway’s game is the best-known example of a cellular automaton. In cellular automata, individual pixels or “cells” are activated in a grid, and very simple rules determine how pixels propagate (or die out). Elaborate patterns can be created and, intriguingly, the Game of Life is Turing complete, just like Ethereum’s Solidity itself. hex6c devised a modification of this game, but based the rules on the luminance in an image. The modified game propagates over an image and modifies its pixels accordingly, summarized in the project notes here:

The effect is as if images are invaded by a colony of artificial life that feeds of pixels, expanding along unpredictable paths, apparently never ending. In fact, since any image has a finite number of pixels, the possible configuration states of the game is also finite, and hence eventually the game repeats itself. However, when this will happen is not easy to predict in advance… (hex6c)

Above, “Invasion 68” is shown as a tribute to photographer Josef
Koudelka. hex6c used Game of Pixel in a few pieces on SuperRare, including this one, the intriguing “Broken Beauty,” and two others.

3. Organic Randomness, SuperRare, 2019

Organic Randomness, SuperRare, 2019

Using the thematics of the Game of Life and his Game of Pixel, hex6c explores how randomness, rules and spatial distribution generate organic structure. It is part of a series of dynamic illustrations by hex6c in 2019, including tributes to the mathematician Hao Wang in “The Tiling Problem,” and a tribute to artist XCOPY in “Beforeglow.”

4. The Primeneeum, SuperRare, 2019

Illustration of a Primeneeum. See SuperRare gallery.

In 2019, hex6c collaborated with Hackatao as “HackHex,” and produced incredible illustrations of the beauty of mathematical structures, in particular the prime numbers:

Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. … Primes are also used in several routines in information technology, such as public-key cryptography, which relies on the difficulty of factoring large numbers into their prime factors. (hex6c)

In collaboration with Hackatao, hex6c devised an algorithm to unfurl prime numbers into a beautiful chain:

We propose an artistic visualization of primes, called Primenuum. The idea behind it is quite simple and came to the beautiful mind of artist Hackatao while thinking at the branching process of natural trees. … Scan the natural numbers starting from 1. For every number, draw a small segment of fixed size, starting from the center of the canvas and moving from left to right. When a prime number is encountered, turn the drawing direction 90 degrees clockwise (alternatively, turn the canvas 90 degrees counter-clockwise). (hex6c)

The algorithm has some similarities to the cellular automata of Game of Life, and results in intriguing fusion of ideas. We see again the spontaneous and the automatic, creating elaborate tree-like structures that emerge from central mathematical concepts.

5. Generative Snail, SuperRare, 2020

Generative Snail, SuperRare, 2020

This piece is simply described on SuperRare: “In fact, I’m just a scatterplot! #generative #R.” hex6c’s pieces often have an element of playfulness, especially earlier work in 2018 and 2019, revealing this kind of early exploration of cryptoart. hex6c also reveals his creation process subtly in the hashtags — statistical programming language R is used to generate a scatterplot. Perhaps the simplest kind of data visualization, a mere scatterplot, yields a mysterious, elaborate structure.

6. Vera Molnár 1/12, SuperRare, 2021

Vera Molnár 1/12, SuperRare, 2021

This is part of a broader project by hex6c. He shares the following note:

This is part of a 12-pieces long series dedicated to Vera Molnár (born 1924), a pioneer of generative art. The series is part of a major project called Generative Art Recode, an effort to preserve pioneering generative artworks by translating them into a modern programming language (Processing). In most cases, the original code underlying these early masterpieces got lost, unfortunately. It is a digital restoration action, using reverse engineering to get the artwork back in a modern day language.

This “recoding” tribute of an early pioneer captivates still, and is especially impressive when considering the efforts that early digital artists invested in creating their work. From hex6c:

Molnár learned the early programming languages of Fortran and Basic, and gained access to a computer at a research lab in Paris where she began to make computer graphic drawings on a plotter. … Disorder in the fault of a system has always evoked Vera Molnár’s interest. She reflected on the influences that a minor implication of disorder had on regular systems and on the role of random in the process of creation.

Again, a fusion of the spontaneous, the automatic.

7. Leo, SuperRare, 2021

Leo, SuperRare, 2021

hex6c shares the following notes for Leo, one of his favorite, and most recent, creations:

Leo is part of the Almagesto project, my latest series dedicated to zodiac signs. Almagesto is a Ptolemaic generative art system that I coded to generate artworks associated with the 12 common known astrological signs: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces. The system closely resembles the motion of the epicycle/deferent scheme, which was proposed in Ptolemy’s Almagest to describe the motions of the planets and stars around the earth and later adopted by Copernicus to describe the motion of the moon around the earth. I coded the system in the Java-based programming language Processing.

The detail on the Almagesto pieces are incredible. The vibrant twists and turns of their elements derived from scientific, technical knowledge, but also embedded in the intriguing lore of astrology — whimsy of the stars:

The saffron-colored helix framing the bright iris in the center gives depth. It is a point that attracts, sucks in, to be feared, where matter is in a continuous state of transformation. The sun’s rays launched outwards distribute gold with generosity and abundance. (hex6c on SuperRare)

Takens Theorem is on Twitter. Disclosure: Takens owns a few hex6c pieces, and has been influenced by hex6c across various projects.



Takens Theorem

Dynamic distributed data displays. Intermittent. Friendly.