Escape Time
A glowing Julia set fractal with filigree spirals in orange, magenta and blue on a dark background

Plate 00 / An independent guide to fractal art

Fractal art, from one equation to a finished print

What fractal art is, how the Mandelbrot set and fractal flames are calculated, which software makes them, how fractals mix with photography and how to print and look after the result.

Dive into the setRead the guides

The fractal art atlas

Pictures calculated, not drawn

Fractal art starts with a rule that is repeated many times. A computer applies the rule to millions of points, turns the results into colour and the artist chooses where to look, which palette to use and how to finish the picture. What is fractal art explains the idea in plain terms, from the origin of the word to the main families of fractals.

The two most famous pictures come from the same formula, z squared plus c. In the Mandelbrot set you vary c and always start at 0. In a Julia set you hold c still and vary the start. The hero above shows a Julia set that follows your pointer, and the plate below dives into the Mandelbrot set itself.

If you want to make something, the software guide compares programs and how to make fractal art gives a step by step workflow. When a picture is ready, read about giclee printing and print care.

Plate 01 / The Mandelbrot set

Dive into the edge of the Mandelbrot set

Scroll to zoom toward a spot in seahorse valley. The readouts show where you are. The detail never runs out, but this demo stops at about 2000 times because the graphics card can only count so finely.

Tightly wound spirals from a deep zoom into the Mandelbrot set, in blue and gold

  1. The whole set

    A main cardioid, round bulbs and a line of smaller copies. Black points never escape.

  2. Seahorse valley

    Between the cardioid and the first bulb the edge curls into spirals that resemble seahorse tails.

  3. Spirals inside spirals

    Every deeper view shows more filaments. Real deep zooms continue far beyond this demo, with special arithmetic.

Plate 02 / Iterated function systems

Build a fern one point at a time

Four simple rules, applied to a point chosen at random with fixed odds. Scroll to plot more points and watch the shape appear. This is the chaos game, the plain ancestor of the fractal flame algorithm.

  • 1 percent of the time the point is squashed onto the stem.
  • 85 percent of the time it shrinks slightly and tilts up the frond.
  • 7 percent of the time it jumps to the left leaflet.
  • 7 percent of the time it jumps to the right leaflet.
A young green fern frond uncurling, its leaflets repeating the shape of the whole frond
The Barnsley fern, a classic example from fractal geometry.

Plate 03 / Nature and the lens

Fractals and photography

Ferns, Romanesco cauliflower, river deltas, frost and tree crowns repeat their shapes at several scales. Real objects do it only approximately and only over a limited range, which makes them good subjects for a camera and a poor match for the pure mathematics.

Fractal art and photography covers how to photograph those patterns, how to place a fractal render over a photo with blend modes and masks, how to build a gradient from the colours of a picture and how to say honestly what is rendered and what is photographed.

Close view of a Romanesco cauliflower with spiral cones repeating at smaller sizes

The atlas index

Nine guides, one plate each

Plate 01

What is fractal art

Where the word comes from, what self similarity means, the main families of fractals and what separates art from a plain plot.

Read the guide

Plate 02

Mandelbrot set explained

The rule z squared plus c, how one point is tested, why colour is a choice and why very deep zooms need more precision.

Read the guide

Plate 03

Julia set vs Mandelbrot set

Both use z squared plus c. One fixes the start and varies c, the other fixes c and varies the start. The home page hero lets you pick c.

Read the guide

Plate 04

Fractal flame algorithm

Random points, weighted transforms, curved variations and log density: the method behind soft, glowing flame pictures.

Read the guide

Plate 05

Fractal art software

Escape time explorers, 3D renderers, flame editors and browser tools, and what to check before you pick one.

Read the guide

Plate 06

How to make fractal art

A seven step workflow from choosing a program to exporting a large file, plus simple ways to start by hand.

Read the guide

Plate 07

Fractal art and photography

Fractal patterns in nature photos, fractal renders as layers and colour sources, and why glass fractal filters are a different thing.

Read the guide

Plate 08

Giclee vs regular print

What the word means, how it differs from photo and office printing, which papers and canvases are used and what to check before ordering.

Read the guide

Plate 09

How to care for giclee prints

Light, glass, humidity, handling and storage: practical care for paper and canvas prints, with the reasons behind each rule.

Read the guide

Quick answers

Questions about fractal art

What is fractal art?
Art made by calculating a fractal, a pattern with detail at every scale, and turning the result into an image. See what is fractal art.
What is the Mandelbrot set in simple terms?
The set of numbers c for which the rule z squared plus c, started at 0, never runs away to infinity. The explanation tests four points by hand.
Do I need special software?
A browser is enough to try a zoom, and several free desktop programs exist for large renders. The software guide compares them.
Is a giclee print worth it?
It can be when colour accuracy and longevity matter. The word has no formal standard, so read giclee vs regular print before you order.