This tool helps to visualize the behavior of functions of complex numbers. Each point on the complex plane between -1-i and 1+i is assigned a color. A function is applied to the point and that color is drawn at the output. This visualization shows each point moving linearly between its input and ending location.

Examples

• f(z) = z2
• f(z) = z3
• f(z) = 1/15 * sin(3.14 * z)
• f(z) = 1/3 * sin(z) / (1+1i)
• f(z) = 1/3 * sin(z) / cos(z)
• f(z) = 1/4 * sin(3.14 * p) * sin(3.14 * p)

You can define simple functions of complex numbers using a simple stack machine notation

• p pushes the input onto the stack.
• + adds the top two elements of the stack and pushes the result to the stack
• - subtracts the top two elements of the stack and pushes the result to the stack
• * multiplies the top two elements of the stack and pushes the result to the stack
• / divides the top two elements of the stack and pushes the result to the stack
• i combines the top two numbers on the stack into a complex number
• s take the complex sine of the top element on the stack
• c take the complex cosine of the top element on the stack
• number pushes the number onto the stack

Debug

Calculations are done on the GPU. Here is the shader code that implements this equation.