// ABOUT
> whoami
A node in the network. Information processing entity.
> cat interests.txt
- :: machine intelligence
- :: distributed systems
- :: cybernetics
- :: accelerationist theory
- :: dark complexity
_
// PROJECTS
// WRITINGS
// THE BACKGROUND
> info reaction_diffusion.system
The patterns behind this page emerge from a Gray-Scott reaction-diffusion system — two coupled partial differential equations simulating chemical reactions:
∂u/∂t = Du∇²u - uv² + F(1-u) ∂v/∂t = Dv∇²v + uv² - (F+k)v
u is substrate, v is activator. Your cursor deposits v. Patterns self-organize through diffusion and reaction. This is literally how Turing patterns form in nature — zebra stripes, leopard spots, coral structures.
> tweak parameters
How fast substrate u is replenished. Higher = more food for patterns.
How fast activator v decays. Higher = patterns die faster.
Spread rate of substrate. Usually 2× Dv for stable patterns.
Spread rate of activator. Lower = sharper patterns.
Presets: F=0.055, k=0.062 (mitosis) | F=0.025, k=0.06 (worms) | F=0.04, k=0.06 (coral)
// LORENZ ATTRACTOR
> info lorenz.system
The Lorenz system — discovered in 1963 modeling atmospheric convection — was the first mathematical demonstration of deterministic chaos. Tiny perturbations lead to wildly divergent outcomes. The butterfly effect.
dx/dt = σ(y - x) dy/dt = x(ρ - z) - y dz/dt = xy - βz
Prandtl number. Affects vortex dynamics.
Rayleigh number. Below 24.74 = stable. Above = chaos.
Geometric factor of convection cells.
// LOGISTIC MAP
> info logistic.bifurcation
The logistic map — one equation, infinite complexity. As r increases: stable point → period-2 → period-4 → ... → chaos. The bifurcation diagram reveals the onset of chaos through period-doubling.
x_{n+1} = r × x_n × (1 - x_n)
r=3.0 → period-2 | r=3.45 → period-4 | r>3.57 → chaos
// JULIA SET
> info julia.fractal
Julia sets — the boundary between escape and capture in the complex plane. For each c, there's a different Julia set. Move your cursor to change c and watch the fractal transform. Infinite detail at every scale.
z_{n+1} = z_n² + c
Move mouse over canvas to change c. Classic values: c=-0.7+0.27i, c=-0.8+0.156i
// CONTACT
- :: email: [your@email.here]
- :: github: [/username]
- :: twitter: [@handle]