Cubic
Symmetry
Engine

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The Art
AKA
The Phenotypes

I grew up on dial-up BBSes and the 3D demoscene. ANSI art in file_id.diz files, MODs and XMs looping off some tracker while a 64k intro melted your 486. So these Forms render real 3D and throw the pixels out, one character per cell. The grid is the medium.

Every Form is one cubic equation. Three roots, always. The discriminant picks the family, the roots decide where everything goes. No noise pretending to be intent. And Ethereum signs with secp256k1, which is a cubic too. Found that through Vitalik’s post on this article and it clicked. The same Δ that sorts every Form into a family is the thing that keeps that curve usable, and a Δ of zero is the one shape it can’t touch. This way, the math securing the chain these Forms will live on is drawn in the characters I grew up with.


  y² = x³ + 7                       Ethereum's secp256k1 curve
  x³ + 0x + 7                       a cubic, p = 0, q = 7

  Δ  = −4p³ − 27q²  = −1323         non-zero, so the curve works
  EC = −16(4a³ + 27b²) = −21168     = 16 × Δ

class: Fractured   one real root, one conjugate pair

Separated8

Δ > 0 · three real roots

Grid, a rendered example
Grid
Lattice, a rendered example
Lattice
Tessellation, a rendered example
Tessellation
Tower, a rendered example
Tower
Strata, a rendered example
Strata
Labyrinth, a rendered example
Labyrinth
Fold, a rendered example
Fold
Prism, a rendered example
Prism

Fractured10

Δ < 0 · one real root, a conjugate pair

Knot, a rendered example
Knot
Exploded, a rendered example
Exploded
Cascade, a rendered example
Cascade
Spiral, a rendered example
Spiral
Shell, a rendered example
Shell
Orbital, a rendered example
Orbital
Weave, a rendered example
Weave
Rift, a rendered example
Rift
Bloom, a rendered example
Bloom
Arbor, a rendered example
Arbor

Merged4

Δ = 0 · a repeated root, the rarest tier

Void, a rendered example
Void
Radial, a rendered example
Radial
Vessel, a rendered example
Vessel
Aperture, a rendered example
Aperture
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