How to Fold a Julia Fractal

Abstraction: Visual intuition for complex numbers through Julia fractal construction

Key points:

• Complex numbers are "numbers that like to turn" — multiplying complex numbers folds the plane by multiplying angles and lengths
• Julia fractals arise from iterating z_{n+1} = z_n^2 + c; different starting values z_1 produce divergent or bounded orbits defining the fractal boundary
• Benoit Mandelbrot used complex number structure to create fractals in the late 1970s
• Complex numbers are essential to quantum physics, electromagnetism, FM radio, wifi — anything involving waves, rotation, or interference
• To fully visualize C→C functions requires 4D; practical visualizations use 3D projections or slices
• The article argues all numbers are "imaginary" in a philosophical sense; the term "imaginary" was historically misleading

Connections: Benoit Mandelbrot · Complex Numbers · Fractals · Julia Set

Source: http://acko.net/blog/how-to-fold-a-julia-fractal/