# 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.
• 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:

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