Fractal Creator

Plain JavaScript

Mandelbrot and Julia fractals with zoom/pan, presets, Multibrot power, colour themes, a Mandelbrot → Julia explorer, PNG export, and a short FAQ/history.

Controls

p=2 is the classic Mandelbrot/Julia.
Controls:
• Mouse wheel: zoom (towards cursor)
• Drag: pan
• Double click: zoom in
• Explorer mode: hover Mandelbrot to set Julia C and update preview

Output

Idle
—
Julia preview
Hover Mandelbrot

FAQ & mini history

How does this page work?
This tool draws fractals by iterating a simple equation for each pixel and colouring based on how quickly the values “escape”.
  • Mandelbrot: each pixel is a different complex number C, and the iteration starts at z₀ = 0.
  • Julia: C is fixed (shown as “Julia C”), and each pixel is a different starting z₀.
What do “Iterations” and “Escape radius” do?
  • Iterations is the maximum number of steps the tool tries before deciding a point is “inside”. Higher values reveal more fine detail, especially when zoomed in.
  • Escape radius is the threshold used to decide that the iteration is diverging. The default 4 works well for classic sets.
What does “Multibrot power (p)” mean?
The classic fractals use z ← z² + C. This tool also supports z ← z^p + C (where p is 2–8).
  • p = 2 → classic Mandelbrot/Julia
  • Higher p values produce different symmetries and “petal-like” structures.
What is the Mandelbrot → Julia explorer doing?
With explorer mode on, hovering over the Mandelbrot image uses the hovered point as the Julia parameter C. The preview canvas then renders the corresponding Julia set for that C value.
In other words: each point of the Mandelbrot set “indexes” a Julia set.
How do zoom and pan work here?
  • Wheel zoom zooms towards your cursor (so you can “dive” into details).
  • Drag pans the view without changing scale.
  • Double-click zooms in quickly.
Tip: increase Iterations as you zoom deeper.
Who was Mandelbrot? And what’s the short history of fractals?
Benoît Mandelbrot (1924–2010) popularised the modern study of fractals and coined the term “fractal” in the 1970s. Earlier work by mathematicians like Gaston Julia and Pierre Fatou (early 1900s) explored related complex dynamics.
Fractals became a home-computer obsession in the 1980s/90s because the pictures are visually striking, the maths is simple to code, and faster CPUs made deeper zooms and higher iteration counts feasible.
Glossary: “escape-time”, “inside”, “boundary”
  • Escape-time: the number of iterations before a point clearly diverges.
  • Inside: points that did not escape within the chosen maximum iterations (often coloured uniformly).
  • Boundary: the complex, infinitely detailed “edge” where tiny changes can switch between escape and non-escape.
Why does colour mode matter if the maths is the same?
Colour is just a mapping from “escape-time” to a palette. Different palettes highlight different structures — but the underlying fractal is unchanged. Monochrome can be clearer for understanding; colour is great for aesthetics.