Melissa Houck

Statement

Spreadsheet Chaos I used Excel to create a grid of complex numbers, then iterated this grid several times using a mapping z2 = f(z1), then used conditional formatting of the absolute value of the final resulting grid. My first print is the result of each iteration raising the previous grid of results to (11+.1i) or (-12-.05i) alternately. In addition, each iteration is multiplied by (4-3i). The 2nd print changed the starting grid using the formula (1-z^4)^-1.5. The 3rd print used the formula (1-z^4)^+1.5 to change the starting grid. The fourth print substitutes a complex tangent for the third iteration.

Artworks

I was inspired after reading Chaos by James Gleick. I used Excel to create a grid of complex numbers, then iterated this grid several times using the mapping f(z2) = z1^2 + c. Using conditional formatting of the absolute value of the final resulting grid of complex numbers, I created a rough facsimile of the familiar Mandelbrot fractal. Why z^2 + c? Why not use a complex power? What about other functions? What if the starting grid were changed? After experimenting with hundreds of combinations and functions, I chose the 4 prints in my submission to show the effect of changing just one variable.