Fractal Engine

A TypeScript library for rendering Mandelbrot and Julia sets with complex mathematical algorithms.

Installation

npm install fractal-engine

Usage

import { renderFractal, mandelbrot, julia } from 'fractal-engine';

const canvas = document.getElementById('canvas') as HTMLCanvasElement;
canvas.width = 800;
canvas.height = 600;

// Render Mandelbrot set
renderFractal(canvas, 'mandelbrot');

// Render Julia set with custom constant
renderFractal(canvas, 'julia', { colorScheme: 'fire' }, { x: -0.7, y: 0.27015 });

Mathematical Background

Mandelbrot Set

The Mandelbrot set is defined by the iterative formula:

$$z_{n+1} = z_n^2 + c$$

where:

• $z_0 = 0$
• $c$ is a complex number representing a point in the complex plane
• The set contains all points $c$ for which the sequence does not diverge to infinity

The escape condition is:

$$|z_n| = \sqrt{z_n \cdot \overline{z_n}} = \sqrt{z_r^2 + z_i^2} > 2$$

Julia Set

The Julia set uses the same formula but with a fixed constant $c$:

$$z_{n+1} = z_n^2 + c$$

where $c$ determines the shape of the fractal. Common values:

• $c = -0.7 + 0.27015i$ (dendrite)
• $c = -0.8 + 0.156i$ (dragon)
• $c = 0.285 + 0.01i$ (swirl)

API

mandelbrot(c, config?)

Calculate Mandelbrot iteration value for a point.

julia(z, c, config?)

Calculate Julia set iteration value.

burningShip(c, config?)

Calculate Burning Ship fractal iteration value.

renderFractal(canvas, type, config?, juliaC?)

Render fractal directly to an HTML canvas.

Configuration

{
  maxIterations: 256,    // Maximum iterations before escape
  escapeRadius: 4,      // Radius at which point is considered escaped
  colorScheme: 'rainbow' | 'fire' | 'grayscale' | 'ocean' | 'sunset',
  offsetX: -0.5,        // Center X coordinate
  offsetY: 0,           // Center Y coordinate
  zoom: 1               // Zoom level
}

Julia Set Presets

import { JULIA_PRESETS } from 'fractal-engine';
// [{ name: 'Dendrite', c: {x: -0.7, y: 0.27015}, ... }, ...]

License

MIT