## The Mandelbrot Set

We must go deeper.

### Options

#### ColorsSet formulas for each RGB value, based on the escape velocity.

#### LocationBounds of image, where *x* is the real axis and *y* is imaginary.

#### IterationsFor more precision, use a higher number, like 1000.

#### How it Works

From Wikipedia:
"The Mandelbrot set is the set of complex numbers *c* for which the function
*f _{c}(z) = z^{2} + c*
does not diverge when iterated from

*z = 0*, i.e., for which the sequence

*f*,

_{c}(0)*f*, etc., remains bounded in absolute value."

_{c}(f_{c}(0))To calculate this I iterate for the number of times specified and see if the result is larger than some threshold number. By increasing the number of iterations, you are more likely to capture whether or not a complex number is part of the set.

The escape velocity (*e* in the color formulas) is determined as the number
of iterations for a given complex number to "escape" and diverge higher
than the chosen threshold. Thus this value is between 0 and the number of iterations.