Melissa Houck

Statement

I enjoy reading “popular math” books that bring mathematical concepts to life in layman’s terms. As an actuary who uses Excel in my work, I find myself using the spreadsheet program to visualize and help me understand the topics I read about. Inspired after reading Chaos by James Gleick, I used Excel to create a rough facsimile of the familiar Mandelbrot fractal by using the mapping f(z2) = z1^2 + c, and iterating it several times, where the z’s are complex numbers. But why z^2 + c? Why not use a complex power? What about other functions, like a trig function? What if the starting grid were changed? What is the impact of making a small change in assumptions?

Artworks

I used Excel to create a grid of complex numbers, then iterated this grid several times using the mapping z2 = z1^[-17+.1i], then used conditional formatting of the absolute value of the grid after each iteration to illustrate it. The starting point is simply a grid of complex numbers with the reals from -1 to 1 and imaginaries from 1 to -1. The photo cube features 6 of the first ten iterations: Iterations 1, 2, 5, 6, 7, and 10, selected for their aesthetics. As you would expect, each iteration is more intricate than the ones before it. It’s interesting to see the changing patterns and colors that each iteration brings.