The Math of the Mandelbrot Set: z²+c, Step by Step
The most complex object in mathematics is built from one short line: z → z² + c. Here is what that formula means, how to run it by hand, and why a five-character rule produces infinite detail.
Complex Numbers
Complex Numbers is a recurring topic across Fractal. This hub collects every guide and explainer tagged Complex Numbers, newest first — each grounded in real mathematics and real examples, written to be rigorous yet readable.
The Mandelbrot Set: Complete Guide (Beginner → Advanced)
The most famous fractal of all, born from the deceptively simple rule z → z² + c. A complete guide from the plain-English intuition to the deep mathematics — connectedness, the cardioid and bulbs, and why its boundary has dimension 2.
Frequently asked
What is Complex Numbers?
Complex Numbers is a topic our editors cover across the site. This hub gathers the related guides and explainers so you can read the full picture in one place.
How often is the Complex Numbers hub updated?
This hub updates automatically whenever a new article is tagged Complex Numbers, so the most recent coverage always appears first.
Who writes the Complex Numbers guides?
Every guide here is written by the Fractal editorial desk, with the mathematics checked against primary sources and explained for a general reader.