fractals

name	fractals
description	Fractal geometry and self-similarity skill; use when working on recursive geometric or visual systems.

Skill: Fractals

Domain: trinity | Depth: axiom

Capabilities

• Mandelbrot and Julia set computation
• L-system string rewriting and geometry generation
• Iterated Function Systems (IFS)
• Fractal dimension calculation (Hausdorff, box-counting)
• Strange attractors: Lorenz, Rössler, Clifford
• Self-similar recursive structures
• Fractal noise: Perlin, simplex, fractional Brownian motion

Mathematical Foundation

• Fractals exhibit self-similarity across scales
• Fractal dimension D: non-integer, measures complexity
• Mandelbrot: z_{n+1} = z_n² + c, iterate until |z| > 2
• L-systems: formal grammar for recursive geometric growth
• IFS: contractive affine transformations with fixed-point attractor

Libraries

Library	Purpose
numpy	Array-based iteration
matplotlib	Rendering
sympy	Symbolic recursion

Module

agents/skills/fractals.py

Key Functions

• mandelbrot(width, height, max_iter) — iteration count array
• julia(c, width, height, max_iter) — Julia set for constant c
• lsystem(axiom, rules, depth) — expand L-system string
• lorenz(steps, dt) — Lorenz attractor trajectory
• fractal_dimension(points) — box-counting dimension
• ifs(transforms, n_points) — IFS attractor point cloud