Generative Art Algorithms

Algorithm	Tags	Key Properties
Value Noise	2D3D	Interpolate random values at grid corners. Simple, slight grid artifacts, cheap
Gradient (Perlin) Noise	2D3D	Interpolate dot products of random gradient vectors. Smoother than value noise. Ken Perlin 1983
Simplex Noise	2D3D	Perlin variant on simplex lattice. Fewer directional artifacts, faster in high dimensions. Perlin 2001
Worley (Cellular) Noise	2D3D	Distance to nearest random point. Produces cell/voronoi pattern. F1, F2-F1, F2 variants
fBm (Fractal Brownian Motion)	Proc	Sum noise at multiple frequencies (octaves). fBm = Σ amplitude * noise(pos * freq)
Domain Warping	Proc	Warp input coordinates by noise before sampling noise. Ingo Quilez technique for organic shapes
Blue Noise	2D	Spectrally uniform distribution — avoids low-frequency clumping. Used in dithering and sampling
Curl Noise	2D3D	Divergence-free velocity field from noise gradient — physically plausible fluid-like flow

Algorithm	Tags	Key Properties
Mandelbrot Set	2D	Escape-time algorithm: iterate z = z² + c. Infinite detail at boundary
Julia Set	2D	Same iteration, fixed c parameter per image. Every point of Mandelbrot spawns a Julia set
Burning Ship	2D	Variant: z = (|Re(z)| + i|Im(z)|)² + c. Ship-like shape
L-Systems	2D3D	String-rewriting grammar for branching structures. Plants, fractals, space-filling curves
IFS (Iterated Function Systems)	2D	Barnsley fern: random affine transforms applied repeatedly. Converges to attractor
Sierpinski Triangle / Carpet	2D	Subdivision fractal. Chaos game: random midpoints. Dimension ≈ 1.585
Koch Snowflake / Curve	2D	Replace each segment middle third with equilateral bump. Perimeter → ∞, area finite
Fractal Terrain (Diamond-Square)	2D3D	Midpoint displacement on height grid. Produces natural-looking mountains

Algorithm	Tags	Key Properties
Conway's Game of Life	2DSim	4 rules on binary grid. B3/S23. Turing complete, gliders, oscillators
General Cellular Automata	2D	Wolfram 1D elementary: 256 rules. 2D generalizations: B/S notation (e.g. B36/S23 = HighLife)
Reaction-Diffusion	2DSim	Gray-Scott model: two chemicals, feed/kill rates control spots, stripes, labyrinths
Smoothed Particle CA	2D	Lenia: continuous Game of Life. Smooth kernel convolution, rich lifelike patterns
Turing Morphogenesis	2D	Activator-inhibitor model for biological patterns (stripes, spots on animal skin). Alan Turing 1952
Belousov-Zhabotinsky	2DSim	Oscillating chemical reaction. Spiral waves, rotating target patterns

Algorithm	Tags	Key Properties
Voronoi Diagram	2D3D	Partition space by nearest seed point. Dual graph = Delaunay triangulation
Delaunay Triangulation	2D	Circumcircle criterion: maximises minimum angles. Bowyer-Watson incremental algorithm
Lloyd Relaxation	2D	Iteratively move Voronoi seeds to centroid of their cell → uniform distribution (blue-noise-like)
Poisson Disk Sampling	2D3D	Minimum distance constraint between points. Bridson fast algorithm: O(N)
Space-Filling Curves	2D	Hilbert curve, Z-order (Morton curve): map 2D to 1D preserving locality
Maze Generation	2D	DFS recursive backtracker, Prim's, Eller's, Wilson's (loop-erased random walk)

Algorithm	Tags	Key Properties
Boids (Flocking)	2D3DSim	3 rules: separation, alignment, cohesion (Craig Reynolds 1987). Emergent murmuration
SPH Fluid	2D3DSim	Particle-based incompressible fluid. Navier-Stokes via kernel interpolation
Lattice-Boltzmann (LBM)	2DSim	Mesoscale fluid: discrete probability distributions on grid. D2Q9, D3Q19 variants
Verlet Cloth	2D3DSim	Distance constraints between particles. Jakobsen position-based dynamics
Strange Attractors	3D	Lorenz, Rössler, Thomas attractors: chaotic ODEs traced as particle paths
DLA (Diffusion-Limited Aggregation)	2D	Random-walking particles stick to cluster. Produces branching fractal (snowflake, coral)

Algorithm	Tags	Key Properties
Signed Distance Functions (SDF)	2D3D	Shape as distance field. Compose with min/max/smoothstep. Ray marching for rendering
Marching Cubes / Squares	2D3D	Isosurface extraction from scalar field. 256 cases (cubes), 16 cases (squares)
Spirographs (Hypotrochoids)	2D	Parametric: rolling circle inside/outside circle. Ratio of radii controls petal count
Chladni Figures	2D	Eigenmodes of vibrating plates: cos(m·x)·cos(n·y) = 0 nodal lines
Supershapes (Superformula)	2D3D	Gielis superformula with 6 parameters generates flowers, starfish, spirals
Lindenmayer Turtle Graphics	2D	L-system strings interpreted as turtle commands (F=forward, +=turn, [=push)