# Mathematical ImageryMathematicians and artists create strong, stunning, works in all media and explore the visualization of mathematics

# Fractal Pancakes :: Nathan Shields

I am a math teacher, illustrator, and dad. Having begun entertaining my children with weekly pancakes earlier this year, I'm always looking for new themes; in this album you'll find some of the fractal pancakes I cooked up one morning. To see about making your own fractal pancakes, as well as other topics I find interesting as a math teacher, check out my blog.

— *Nathan Shields*

A Lorenz attractor comes from a system of three differential equations created to model convection in the atmosphere, and frequently used to show the sensitivity of a chaotic system to initial conditions. For another chaotic system, invite your kids to help design the pancakes.

The Mandelbrot Set, which is one of the tastiest fractals, is the collection of points c on the complex plane which allow the iterated transformation z = z^{2}; + c to remain within a given threshold. I've always been awestruck by the infinite complexity that springs from that simple equation.

This fractal, like many others, is fun to doodle at faculty meetings. Here, each triple of touching squares encloses a right triangle in a traditional visualization of the Pythagorean Theorem.

A Sierpinski triangle is a fractal, a structure that displays self-similarity at various scales. This fractal is created by recursively removing triangular pieces from the structure indefinitely - of course, the pancake isn't very hearty if you really do this, but you get the idea.