CypherDAO

"Parental Advisory: Explicit Yul Content. You and people around you may be exposed to content that you find objectionable and/or offensive. All stunts were performed by trained professionals, don't try this at home." That's an actual comment in the Strange Attractors source code. It sits right above the part where @cxkoda solves differential equations in raw EVM assembly. We spent this week reviewing the full contract system for this project again, all three layers of it. Here's what's actually happening when you look at one of these, because we don't think most people know. Even holders. TL;DR: Strange Attractors, @cxkoda, October 2021 • Every render means the EVM numerically solving chaotic differential equations. Runge-Kutta 4, real computational physics, hand-written in assembly • The EVM has no sin, cos, or sqrt. So he built trigonometry from scratch, in the contract. π is stored on-chain as a 96-bit fixed-point integer • The smooth curves aren't smoothing. The renderer uses the equations' own derivatives as Bézier handles. The physics draws itself • Holders can move the camera, recolor, and re-render. • Interactivity at contract level. • No server, no stored image, no script in your browser. • Ask the chain, it computes the artwork again. Every time. Forever • Minted in 2021, a very special historical window that produced Brotchain @divergencearran and @divergenceharri, Cypher @TsukamotoHideki, Loot @dhof, solSeedlings @dievardump, Terraforms @mathcastles, @_deafbeef's generative audiovisual series and others. We believe that window was not an accident! • Written entirely by hand in 2021, before AI coding assistants existed. Every opcode of this was one person and a problem. That kind of authorship is now datable, like brushwork When a Strange Attractor renders, the EVM numerically integrates a system of chaotic differential equations. Not "references a stored image." Not "runs a script in your browser." The chain runs a Runge-Kutta 4 integration, the workhorse scheme of computational physics. For the Huang Multi-Wing system that's 6,656 timesteps per render, and each of the five systems carries its own parameters, inscribed permanently in its setup transaction. The solver is hand-written assembly because Solidity alone would be too expensive. The EVM has no math library. No sine. No cosine. No square root. So he built them. MathHelpers.sol implements trigonometry from scratch as Taylor series, with hand-derived fixed-point coefficients and documented error bounds ("absolute error <1e-3"), plus square root via the Babylonian method with fixed iterations so gas stays predictable. π is stored in the contract as 248902613312231085230521944622. Why does every edition of the same system look different? Fibonacci sphere lattices. The contract computes quasi-evenly distributed points on a sphere and each edition gets its own camera angle onto the attractor. The viewing direction is math too. And the curves: the solver outputs not just points but tangents, the actual derivatives of the dynamical system, and the renderer uses them as Bézier control handles. The smooth lines aren't smoothing. They're the equations' own slopes shaping the path. It's interactive at the contract level too. Holders can set their own projection axes, colors, and render size, directly on-chain. You don't own a picture of a simulation. You own a view into one, and you can move the camera. One precision worth stating: the contract recomputes all of this every time it's asked. Marketplaces cache the result and rarely ask again, but that's a fact about marketplaces, not the artwork. Call tokenURI yourself, free, and the chain solves the equations again. The cached thumbnail is a convenience. The mathematics is the artwork. And because we believe in reading the whole contract: there's an owner-only function called rerollTokenRandomSeed, and its comment explains itself with total honesty. It exists as "a last resort" in case a seed produces values that don't converge to the attractor. "Although this never happened while testing, you never know for sure with random numbers." An escape hatch against mathematics itself, documented in deployed source. That's artist integrity at the bytecode level. Class III in our working taxonomy (v0.1), On-Chain Simulated System, is exactly this: the chain doesn't store the art or point at the art. It computes the art, live, from its own physics, every time you ask. Maybe a handful of projects in existence operate at this technical depth. This is one of them. Disclosure: CypherDAO holds Strange Attractors.