This is a test in how exponents can affect a picture on a coordinate plane when using complex numbers. Given any point (x, y), it can be represented by complex number x+yi, where I=sqrt(-1). Press space to switch between two different modes of two different complex functions. #1: this function takes a point (x, y), makes it into x+yi, and raises it to a power. There is a general formula where x+yi can be converted into r*(cos(t)+i*sin(t)), where r is the length from the origin to the point the complex number represents, and t is the angle from the positive x-axis to the point. The formula, which is De Moivre's theorem, states that (x+yi)^n=(r^n)*(cos(tn)+I*sin(tn)), making it easy to raise any complex number to any real power. #2: this function now takes (x, y) to x+yi, and raises a real number to that power. Basically it is raising a number to a complex power. Computing this requires using Euler's theorem, but it is possible, and inside this project it has a general formula for doing so.
Online research. Search "complex exponentiation" to research about raising a number to a complex power.
