# Mandelbrot Set Calculator for Fractals, Escape Time, and Self-Similarity
This Mandelbrot fractal calculator renders the classic complex-plane set defined by the iteration z(n+1) = z(n)^2 + c. It is designed for exploration rather than passive viewing: every click recenters the plane, each zoom exposes a smaller mathematical neighborhood, and the iteration slider lets you decide how deeply the calculator should test the boundary before coloring a point as stable or escaping.# How to Read the Mandelbrot Image
The dark central shape marks points whose orbits remain bounded within the current iteration budget. The colored exterior is an escape-time map. A point colored close to the set may survive hundreds of iterations before its magnitude exceeds the escape radius, while a point far away escapes almost immediately. The most scientifically interesting geometry is usually not inside the filled shape, but along the boundary where bounded and unbounded behavior interlace.| Control | What it changes | When to increase it |
|---|---|---|
| Iteration depth | How many recurrence steps are tested for each pixel. | Use higher values after zooming into thin filaments or miniature copies. |
| Escape contrast | How strongly smooth escape values are separated into visible bands. | Raise it when the image looks flat; lower it when colors are too harsh. |
| Palette | The color mapping applied to outside points. | Switch palettes to reveal structures that may be hidden by one color field. |