| Type: | Package |
| Title: | Generates Views on the Mandelbrot Set |
| Version: | 0.2.0 |
| Description: | Estimates membership for the Mandelbrot set. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 6.0.1 |
| Imports: | reshape2 |
| Suggests: | testthat, RColorBrewer |
| NeedsCompilation: | yes |
| Packaged: | 2017-07-06 07:16:26 UTC; benmoore |
| Author: | Ben Moore [aut, cre], Mario dos Reis [aut] |
| Maintainer: | Ben Moore <ben@blm.io> |
| Repository: | CRAN |
| Date/Publication: | 2017-07-06 10:06:55 UTC |
Convert Mandelbrot object to data.frame for plotting
Description
Converts objects produced by mandelbrot
to tidy data.frames for use with ggplot and other tidyverse packages.
Usage
## S3 method for class 'mandelbrot'
as.data.frame(x, ...)
Arguments
x |
a Mandelbrot set object produced by |
... |
ignored |
Value
a 3-column data.frame
Examples
mb <- mandelbrot()
df <- as.data.frame(mb)
head(df)
Calculate the Mandelbrot set
Description
Generates a view on the Mandelbrot set using an underlying C function.
Usage
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 |
iterations |
maximum number of iterations to evaluate each case |
Details
mandelbrot0 is an experimental interface
for generating tidy data.frames faster than
as.data.frame(mandelbrot()).
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
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
https://stat.ethz.ch/pipermail/r-help/2003-October/039773.html http://people.cryst.bbk.ac.uk/~fdosr01/Rfractals/index.html
Generate palette suitable for coloring a set
Description
Takes a simple palette and expands / oscillates it for use with Mandelbrot sets.
Usage
mandelbrot_palette(palette, fold = TRUE, reps = 1L, in_set = "black")
Arguments
palette |
vector of color hex strings (e.g. '#FFFFFF') |
fold |
wrap or fold the palette back on itself |
reps |
number of times to replicate the color vector |
in_set |
color for areas in the Mandelbrot set |
Value
an extended color vector
Examples
view <- mandelbrot(xlim = c(-0.8438146, -0.8226294),
ylim = c(0.1963144, 0.2174996), iter = 500)
# can be used to simply interpolate a color gradient
spectral <- RColorBrewer::brewer.pal(11, "Spectral")
cols <- mandelbrot_palette(spectral, fold = FALSE)
plot(view, col = cols, transform = "inv")
# simple palettes might need folds / reps to look good
blues <- RColorBrewer::brewer.pal(9, "Blues")
cols <- mandelbrot_palette(blues, in_set = "white",
fold = TRUE, reps = 2)
plot(view, col = cols, transform = "log")
Plot a Mandelbrot set using base graphics
Description
Draws colored set membership using image.
Usage
## S3 method for class 'mandelbrot'
plot(x, col = mandelbrot_palette(c("white",
grey.colors(50))), transform = c("none", "inverse", "log"), asp = 1, ...)
Arguments
x |
an object generated by |
col |
a vector of colors, such as those generated by
|
transform |
the name of a transformation to apply to the number of iterations matrix |
asp |
the |
... |
extra arguments passed to |