Calculate the Mandelbrot set

Generates a view on the Mandelbrot set using an underlying C function.

mandelbrot(xlim = c(-2, 2), ylim = c(-2, 2), resolution = 600,
  iterations = 50)

mandelbrot0(xlim = c(-2, 2), ylim = c(-2, 2), resolution = 600,
  iterations = 50)

Arguments

xlim	limits of x axis (real part)
ylim	limits of y axis (imaginary part)
resolution	either an integer $n$ for $n^2$ pixels or a list with x and y components specifying the resolution in each direction (e.g. `list(x = 500, y = 500)`)
iterations	maximum number of iterations to evaluate each case

Value

a mandelbrot structure with components: x a vector of the real parts of the x-axis; y the imaginary parts of each number (the y-axis); z a matrix of the number of iterations that $|z|<2$

Details

mandelbrot0 is an experimental interface for generating tidy data.frames faster than as.data.frame(mandelbrot()).

Mandelbrot set

In brief, the Mandelbrot set contains the complex numbers where the 0 orbit of the following function remains bounded ($<2$): $$f_{z+1} = z^2 + c$$

For information and discussion on the Mandelbrot and related sets, one great resource is plus.maths.org. There's also a popular YouTube video by Numberphile.

Credits

Wraps original C code by Mario dos Reis, September 2003.

References