# Stefan Samociuk

Artist
Penlon Farm
Llanarth, Ceredigion, Wales UK

When you do sums, whether on a hand calculator, a huge sum on a super computer or some geometry with a compass and ruler, where does the answer come from? This is something that has puzzled me since childhood. When working as project chief at the French computer graphics society in Paris, this puzzlement associated with sums expanded into computer generated geometric patterns. Is there a fundamental connection between form and number? I now believe there is and it originates with prime numbers containing a geometric structure, their signature geometry, unique for each and all primes. We can compute these signature geometries in all prime number dimensional spaces with the transcendent form transcode algorithm, TTA.

A prime 29 photonic crystal
50 x 50 cm
Textile
2016

I study tens of thousands of geometric structures to learn how the landscape of prime signature geometries changes between primes and the variables of the TTA. Similar to a painter, this learning is about experimentation, add something here, try this try that, stand back and see the change. Certain geometries evoke a sensation similar to when I look at a block of computer code or an engineering schematic, a purpose, a machine function. As linear transcodes generate periodic geometries based on the prime magnitude employed, my next artistic venture is to nano engineer this graphic into a photonic crystal, PC, and see how it manipulates light, the “Arabian Opal”. Blue pixels represent hole position in the PC substrate. Based on prime 29.

Kandinsky's challenge to Gauss.
50 x 50 cm
Textile
2016

The level of abstraction in this transcode caused me to imagine a dialogue between the mathematician Gauss and the modern artist Kandinsky. The artist was a critic of the geometric graphics derived purely from prime numbers. Too much “meaning and function”, this was the domain of art and intelligence, not number. Gauss must have drawn them with his own hand. How could Gauss convince the artist that number was indeed the agent of the geometries he demanded? “Show me a geometric structure that’s a cubic light year square” replied Kandinsky, “Done” said Gauss,”but” continued the artist, “base it on a trillion digit prime in a billion dimension space, then show me a 3D section”. “I need a bigger computer” pondered Gauss. Based on prime 23.