Valerie Russell

Unit 6

Imaginary Numbers

By Natasha Cline, Margaret Songster, Malika Thompson, and Victoria Randall

When we were studying imaginary numbers, Ms. Russell told us about the "Mandelbrot" set and how it marks and iterates a set of points in the complex plane. It is obtained from a recurrence equation. In a recurrence equation, a pattern needs to be replicated or iterated over and over again. To iterate a function, input a starting value and solve the function. Then input the solution into the same function and solve again. Notice how the pattern in our design repeats itself but gets smaller and smaller.

Using technology we created this beautiful design for a Mandelbrot set. It was quite easy. We took the picture and divided it into 4 quadrants modeling a complex plane. Symmery was involved and some algebra. We learned how to add, subtract, multiply, divide and graph complex numbers in the form a+bi.