Mandelbrot convergence counts

Mandelbrot convergence counts

mandelbrot(...)

# S3 method for matrix
mandelbrot(Z, maxIter = 200L, tau = 2, ...)

# S3 method for numeric
mandelbrot(
  xmid = -0.75,
  ymid = 0,
  side = 3,
  resolution = 400L,
  maxIter = 200L,
  tau = 2,
  ...
)

Arguments

Z

A complex matrix for which convergence counts should be calculated.

maxIter

Maximum number of iterations per bin.

tau

A threshold; the radius when calling divergence (Mod(z) > tau).

xmid, ymid, side, resolution

Alternative specification of the complex plane Z, where mean(Re(Z)) == xmid, mean(Im(Z)) == ymid, diff(range(Re(Z))) == side, diff(range(Im(Z))) == side, and dim(Z) == c(resolution, resolution).

Value

Returns an integer matrix (of class Mandelbrot) with non-negative counts.

Author

The internal Mandelbrot algorithm was inspired by and adopted from similar GPL code of Martin Maechler available from ftp://stat.ethz.ch/U/maechler/R/ on 2005-02-18 (sic!).

Examples

counts <- mandelbrot(xmid = -0.75, ymid = 0, side = 3)
str(counts)
#>  'Mandelbrot' int [1:400, 1:400] 1 1 1 1 1 1 1 1 1 1 ...
#>  - attr(*, "params")=List of 3
#>   ..$ Z      : cplx [1:400, 1:400] -2.25-1.5i -2.25-1.49i -2.25-1.48i ...
#>   ..$ maxIter: int 200
#>   ..$ tau    : num 2
if (FALSE) {
plot(counts)
}

if (FALSE) {
demo("mandelbrot", package = "future", ask = FALSE)
}