mandelbrot: Mandelbrot convergence counts

In future: Unified Parallel and Distributed Processing in R for Everyone

Mandelbrot convergence counts

Description

Mandelbrot convergence counts

Usage

mandelbrot(...)

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

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

Arguments

Z	A complex matrix (Z) for which convergence counts (C) should be calculated.
maxIter	Maximum number of iterations (c^{max}) per bin.
tau	A threshold (\tau); the radius when calling divergence (|z_{i}| > \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 (C).

Escape time algorithm

The convergence counts are calculated using the standard escape-time algorithm for the Mandelbrot set: for each complex number c, the sequence z_{i+1} \leftarrow z_{i}^2 + c (starting at z_{0} = c) is iterated until either its modulus (|z_{i}|) exceeds the escape radius \tau (tau) or the maximum number of iterations (c^{max}) has been reached. The count (c_{i}) recorded is the iteration at which the sequence escaped, or c^{max} for points that never escaped.

References

Mandelbrot set, https://en.wikipedia.org/wiki/Mandelbrot_set, 2026

Examples

counts <- mandelbrot(xmid = -0.75, ymid = 0, side = 3)
str(counts)
## Not run: 
plot(counts)

## End(Not run)

## Not run: 
demo("mandelbrot", package = "future", ask = FALSE)

## End(Not run)

future documentation built on Sept. 24, 2026, 5:12 p.m.