mandelbrot

as.raster.Mandelbrot

plot.Mandelbrot

mandelbrot_tiles

mandelbrot.matrix

mandelbrot.numeric

internal

The purpose of this package is to provide a lightweight and
unified Future API for sequential and parallel processing of R
expression via futures. The simplest way to evaluate an expression
in parallel is to use `x %<-% { expression }` with `plan(multisession)`.
This package implements sequential, multicore, multisession, and
cluster futures. With these, R expressions can be evaluated on the
local machine, in parallel a set of local machines, or distributed
on a mix of local and remote machines.
Extensions to this package implement additional backends for
processing futures via compute cluster schedulers, etc.
Because of its unified API, there is no need to modify any code in order
switch from sequential on the local machine to, say, distributed
processing on a remote compute cluster.
Another strength of this package is that global variables and functions
are automatically identified and exported as needed, making it
straightforward to tweak existing code to make use of futures.

Henrik Bengtsson

future

Unified Parallel and Distributed Processing in R for Everyone

mandelbrot function

<dl><dt>Z</dt>
<dd>A complex matrix (\(Z\)) for which convergence
counts (\(C\)) should be calculated.</dd>
<dt>maxIter</dt>
<dd>Maximum number of iterations (\(c^{max}\)) per bin.</dd>
<dt>tau</dt>
<dd>A threshold (\(\tau\)); the radius when calling
divergence (\(|z_{i}| &gt; \tau\)).</dd>
<dt>xmid, ymid, side, resolution</dt>
<dd>Alternative specification of
the complex plane <code>Z</code>, where
<code>mean(Re(Z)) == xmid</code>,
<code>mean(Im(Z)) == ymid</code>,
<code>diff(range(Re(Z))) == side</code>,
<code>diff(range(Im(Z))) == side</code>, and
<code>dim(Z) == c(resolution, resolution)</code>.</dd></dl>

Arguments

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 \(\tau\) (<code>tau</code>) 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.

Escape time algorithm

Mandelbrot convergence counts — mandelbrot

<dl>

<dt>Z</dt>
<dd>A complex matrix (\(Z\)) for which convergence
counts (\(C\)) should be calculated.</dd>


<dt>maxIter</dt>
<dd>Maximum number of iterations (\(c^{max}\)) per bin.</dd>


<dt>tau</dt>
<dd>A threshold (\(\tau\)); the radius when calling
divergence (\(|z_{i}| &gt; \tau\)).</dd>


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

</dl>

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 \(\tau\) (<code>tau</code>) 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.

mandelbrot: Mandelbrot convergence counts

Description

Usage

Value

Arguments

Escape time algorithm

References

Examples