This tweet was retweeted by Steve Strogatz:

@stevenstrogatz great @Mathologer video on the cardioid and its family: https://t.co/ElDxW67N3X

— 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 Set viewed through Pre-Calculus. Presentation, Lesson Plans, and Interactives. Links to the various blog posts are at the bottom of the page.
• Processing Experiments:
  • Waning Moon – Steps through linear functions with slope 1 to 4.
    
  • Interactive Waning Moon – Uses the mouse to control the slope and the y-intercept of the linear function.
    
  • Linear Waning Moon – Interactive. Same process, but instead of a circle, inputs are in a line at the top and outputs are in a line at the bottom.
    
  • Linear Mod Art – Interactive, similar setup as above, but useful for teaching how it works.
    
  • Sine Mod Art – Same as above, but using a sine function instead of a linear function.
    
  • Waning Sine Moon – Interactive circular version using sine.
    
  • Waning Exponential Moon – Interactive circular version using an exponential function.
    

The nice thing about the processing versions is you can pretty easily create large image files that you can print: