Linear Functions, Cardiods, and the Mandelbrot Set

This tweet was retweeted by Steve Strogatz: @stevenstrogatz great @Mathologer video on the cardioid and its family: — Anna Lukács (@launknaacs) November 6, 2015 What a great video, linking linear functions, cardiods, and the family of Mandelbrot sets. Rang my bell. Here’s some of my previous lessons and experiments that involved these things: The Mandelbrot […]

The Mandelbrot Set Viewed through Precalculus

I’ve given this presentation in November 2014 at AMTNYS in Syracuse, and in April 2015 at NCTM in Boston. I’ll be giving the presentation in May 2015 at the NY Master Teacher Conference, and in July 2015 at Twitter Math Camp in Claremont CA.  Drive Why use the Mandelbrot fractal to get the students to […]

Mandelbrot Fractal v2

I had so much fun with the original Mandelbrot program that I decided to see if I could improve it. I was amazed by how easily I was able to generate a fractal picture that looked exactly like other pictures online. I didn’t look at anyone else’s code, just went down the path and the amazing […]

Mandelbrot Fractal

I was inspired by a My Favorite presentation from a student on the Mandelbrot fractal. I played around for a half hour at school without a ton of success, but I sorted out the sticking points on the way home, and finished it up tonight. Amazingly simple (the code may not look simple, but it’s […]

Chaos Game v2

I prepared a small demonstration of the Chaos game for some math teachers. First we used transparencies, markers, dice, and rulers, but humans are mistake-prone and slow. To The Computer! I decided to experiment with the rules of the game to see where it’d go. Human Error What happens when you bring in a random amount […]

Chaos Game

The chaos game, previously seen on Frank Noschese’s 180 blog and Jonathan Clayton’s blog Infinite Sums. I had to make this myself (deja vu?). Here’s what I made (processing 2.0): Check it out live. All these live links will probably work great on your smartphone too. Source code. Variations Random Triangle Chaos game. Click to set […]

Fractal Brownian Tree

@fawnpnguyen whoa. Need to try and make this. — Dan Anderson (@dandersod) June 4, 2013 I started off and used VPython to create the fractal, but it was slow and buggy. Here’s a movie of my first attempt. When you click you create a new “seed” for the fractal to start.  So I rewrote it […]