Make Your Own Mandelbrot

by Tariq Rashid

A gentle journey through the mathematics of the Mandelbrot and Julia fractals, and making your own using the Python computer language.

Mathematics can be fun, exciting, surprising, and stunningly beautiful. But too few people ever experience this, associating it instead with boring and apparently pointless exercises in trigonometry and solving equations.

This guide will take you on an emotional journey, starting from very simple ideas, and exploring some surprising and intricately beautiful behaviors of the very simple mathematics that underlies the famous Mandelbrot fractal. You won't need anything more than basic school mathematics.

Part 1 is about ideas. It introduces the mathematical ideas underlying the Mandelbrot fractal, gently with lots of illustrations and examples.

Part 2 is practical. It introduces the popular and easy to learn Python programming language, and gradually builds up a program to calculate and visualise the Mandelbrot fractal.

Part 3 extends these ideas. It reveals the related Julia fractals, creates 3-dimensional landscapes and shows how even more interesting images can be made using mathematical filters.

The fractal image on the cover of this book is created using only the ideas and code developed in this book.

134 pages, Kindle Edition

First published April 2, 2014

Reviews

[Donald Hardy · Rating 5 out of 5]

Rashid's book is saving my sanity during the COVID-19 inflected newest version of culture wars in America. Don't want to think twenty-four hours a day about who is or isn't leading the country? Read this book and think instead at least some of the time about mathematical recursion, iteration, complex numbers, the complex plane, chaos, computer art, fractal patterns in nature and what it all could mean or not mean. People sometimes refer to the Mandelbrot set as the hand print of God. I don't know if it's all that, but it's at least some of that, at least the thumbprint of God. Rashid explains in maddeningly unproofread prose not only the simple mathematics behind Mandelbrot and Julia patterns, but also how to program both in Python. Rashid does not cover Geogebra, but it (free on the internet) provides an environment to explore some of the corners of these patterns. Rahid's is a fascinating book and (besides the proofreading) a well written book.

[Diego A. · Rating 5 out of 5]

DYI intro to fractals

I loved this quick and easy intro to fractals through python. With very clear and simple math and programming, the book gets you plotting the Mandelbrot set in a few minutes.
Thanks!

[Jimmy · Rating 4 out of 5]

this was a great little book that shows how chaos, complex numbers, and programming can all be done with simple maths and a lot of fun!

[Kensuke Nakai · Rating 5 out of 5]

Easy to understand and awesome

I really enjoyed this awesome Mandelbrot guide. I also love the concept of this book which is just for fun. Thanks a lot for the great story!

[Roberto Rigolin F Lopes · Rating 4 out of 5]

Thrilling "how to" with striking plots. Emphasis on striking because "spectacular" also works. Tariq did a great job making fractals accessible to layperson. The whole journey is simple + intriguing. Seems that nature is all about simple computations iterated many many times.