Complex numbers are often introduced by way of the mysterious imaginary number i (the square root of -1). But beginning with i is not the best way to give beginners an intuitive sense of what complex numbers really are, and why they are so awesome.
The Dragon of Eve is a plane-filling, self-avoiding fractal curve, which I discovered in the 1980's, and named for my mother's Art teacher, Eve Peters. This video shows how the curve is fractalized, and compares it to other similar curves, including the classic dragon curve.
Each number branches from its largest divisor
A particle swarm finds the boundary of the Mandelbrot Set