Linear Functions, Cardiods, and the Mandelbrot Set

This tweet was retweeted by Steve Strogatz:


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.
      2015-11-09_08h31_23
    • Interactive Waning Moon – Uses the mouse to control the slope and the y-intercept of the linear function.
      2015-11-09_08h29_26
    • 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.
      2015-11-09_08h29_54
    • Linear Mod Art – Interactive, similar setup as above, but useful for teaching how it works.
      2015-11-09_08h30_52
    • Sine Mod Art – Same as above, but using a sine function instead of a linear function.
      2015-11-09_08h32_37
    • Waning Sine Moon – Interactive circular version using sine.
      2015-11-09_08h33_58
    • Waning Exponential Moon – Interactive circular version using an exponential function.
      2015-11-09_08h35_05

The nice thing about the processing versions is you can pretty easily create large image files that you can print:
IMG_2083
IMG_2084

 

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