How to create the Mandelbrot set


The Mandelbrot set is possibly the most reproduced mathematical entity of all time, on account of how with a bit of image processing, you can make extremely pretty and interesting pictures with it.
But how does it work? The set has dizzying mathematical depth, but it turns out the rules for creating it are fairly straightforward. To get the idea, all you need is a rough understanding of iteration, convergence, and complex numbers.
Dr. Holly Kreiger from MIT shows us how below (interspersed with some of the famous Mandelbrot zoom shots, of course). Check it out. --Ryan Cooper
Subscribe to The Week
Escape your echo chamber. Get the facts behind the news, plus analysis from multiple perspectives.

Sign up for The Week's Free Newsletters
From our morning news briefing to a weekly Good News Newsletter, get the best of The Week delivered directly to your inbox.
From our morning news briefing to a weekly Good News Newsletter, get the best of The Week delivered directly to your inbox.
Sign up for Today's Best Articles in your inbox
A free daily email with the biggest news stories of the day – and the best features from TheWeek.com
Ryan Cooper is a national correspondent at TheWeek.com. His work has appeared in the Washington Monthly, The New Republic, and the Washington Post.
-
5 worm-ridden cartoons about RFK. Jr and the CDC
Cartoons Artists take on vaccine advisers, medical quackery, and more
-
Will 2027 be the year of the AI apocalypse?
A 'scary and vivid' new forecast predicts that artificial superintelligence is on the horizon A 'scary and vivid' new forecast predicts that artificial superintelligence is on the horizon
-
Crossword: June 15, 2025
The Week's daily crossword puzzle
-
Nobody seems surprised Wagner's Prigozhin died under suspicious circumstances
Speed Read
-
Western mountain climbers allegedly left Pakistani porter to die on K2
Speed Read
-
'Circular saw blades' divide controversial Rio Grande buoys installed by Texas governor
Speed Read
-
Los Angeles city workers stage 1-day walkout over labor conditions
Speed Read
-
Mega Millions jackpot climbs to an estimated $1.55 billion
Speed Read
-
Bangladesh dealing with worst dengue fever outbreak on record
Speed Read
-
Glacial outburst flooding in Juneau destroys homes
Speed Read
-
Scotland seeking 'monster hunters' to search for fabled Loch Ness creature
Speed Read