Choose one of the four three.js visualizations below, each module is interactive, play around with the parameters and explore the fascinating world of fractals!
Mandelbrot Set Visualization with Click-to-Julia Zoom
What is shown: This view renders the Mandelbrot set in the complex plane and lets you click points to inspect the corresponding Julia behavior and local structure.
How it works: A GPU fragment shader iterates z_{n+1} = z_n^2 + c per pixel, applies smooth coloring from escape-time values, and updates the center/zoom interactively from pointer events.
Math background: The Mandelbrot set is the set of c ∈ ℂ where the orbit of z_0 = 0 under z → z^2 + c stays bounded; picking a c defines a related Julia set and illustrates parameter-space versus dynamical-space structure.
Interactive Julia Set Browser
What is shown: This visualization shows 2D Julia sets for different complex parameters and reveals how fine boundary detail changes with zoom and parameter shifts.
How it works: The shader computes repeated complex squaring with a fixed c, then maps iteration depth to a color palette with optional animated cycling for visual contrast.
Math background: For fixed c, the Julia set is the boundary between points whose orbits under z → z^2 + c remain bounded and those that escape; connectedness and geometry vary strongly with c.
3D Mandelbulb Fractal
What is shown: This panel displays a volumetric 3D fractal analogous to Mandelbrot-style dynamics, revealing spirals, lobes, and self-similar detail in space.
How it works: It uses distance-estimated ray marching in a fragment shader, plus camera controls and post-processing bloom to render a real-time lit implicit surface.
Math background: The Mandelbulb generalizes escape-time iteration to spherical-coordinate power maps in ℝ^3; points are classified by whether iterates escape beyond a bailout radius.
3D Quaternion Julia Set Visualization
What is shown: This view presents a 3D slice of a quaternion Julia set, producing intricate surfaces that extend Julia dynamics beyond the complex plane.
How it works: The renderer evaluates quaternion iterations in shader code, estimates distance fields, and ray marches the implicit fractal while exposing key constants for exploration.
Math background: Quaternion iteration extends z → z^2 + c to four-dimensional algebra; visualized 3D slices capture bounded-orbit structure and reveal higher-dimensional fractal geometry.