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.

Ever since he was a kid, Tariq has loved the beauty and excitement of science, maths and computing.

He devoured everything he could get his hands on in the libraries near his home, in England, especially books on fractals and programming the BBC micro ... this was a long time before the world wide web!

Despite all the fun and adventures over the 30 years since then, he still thinks too many amazing ideas are badly explained. His personal mission is to do the hard work to make beautiful exciting ideas simple and accessible enough for anyone to understand and appreciate.

He has a degree in Physics, a Masters in Machine Learning and Data Mining, is active in London's tech scene, leads the London Python meetup group (almost 3000 members) and loves doing talks/workshops whenever he can. For a day job, he works mostly in technology and digital strategy, but really he's trying to introduce design thinking. He loves open source, and was lucky enough to lead on open source reform for the UK Government.

More importantly, he has an amazing wife and a cute clever daughter who seems to have inherited the genes for loving art from both parents.