This tool visualizes repeated applications of complex functions. You can explore the classic Mandelbrot and Julia sets, as well as create your own custom complex functions.

We define a complex-valued function f(z). We start out with an initial z-value z₀, repeatedly apply f(z), and color pixels based on where the sequence goes.

Enter GLSL code that returns a vec2 result. Your function should use the variables z and c which are both vec2 (complex numbers).

Available complex functions:

• a + b (you can just use + for addition)
• csquare(z) : z²
• ccube(z) : z³
• cpow(z, n) : z^n
• cmul(a, b) : a * b
• cdiv(a, b) : a / b
• csin(z), ccos(z)
• cexp(z), clog(z)

There are two coloring modes:

• Escape: Pixel color is based on how many iterations it takes for the sequence to blow up to infinity. The color is black if the sequence stays bounded.
• Convergence: Pixel color is based on where the sequence converges to. If the sequence converges, the pixel's hue is based on the angle of the limit. The pixel is black if the sequence does not converge.

By default, we have parameters z₀ and c. z₀ is special and controls the initial value of the sequence, and c is just a parameter of the function.

You can add additional custom parameters to use in your function.

1. Enter a name (e.g., "p"), real and imaginary values
2. Click Add
3. Use the parameter in your function directly by its name (e.g., if you named your parameter "p", just use p in your function)

For each parameter, you can choose between two modes:

• Dot: Allows you to drag a colored dot to set the value
• Pixel: For each pixel, the value is the pixel position

Example: If you create a parameter named "p", refer to it simply as p in your function:

return csquare(z) + cmul(c, p);

• +/-: Increase/decrease the maximum number of iterations
• r: Reset view