Fractal Image Data Generator

Generates image data for fractals (Julia and Mandelbrot sets) on the complex plane in the given region and resolution. Benoit B Mandelbrot (1982).

Julia

Julia: Fractal Image Data Generator

The package aim at generating Julia and Mandelbrot sets with given initial conditions and resolution using an escape time algorithm. A resulting data matrix is represents escape times at each matrix entry.

Julia Set

Julia set data can be generated with the JuliaImage function. An example case,

imageN <- 2000
centre <- 0.0
L <- 4.0
C <- -0.8 + 0.156i
image_matrix <- JuliaImage(imageN, centre, L, C)

A sample visualisation with R's hcl palette Roma as set values on a grid given as a matrix.

par(mar=c(0, 0, 0, 0))
image(image_matrix[550:1450, 200:1800], 
      col=hcl.colors(2000, palette="Roma"), 
      axes=FALSE, useRaster=TRUE)

Mandelbrot set

Mandelbrot set data can be generated with MandelImage function.

An example to generate the data:

imageN <- 2000; 
centre <- 0.0
L <- 4.0
image_matrix <- MandelImage(imageN, centre, L);

A sample visualisation with R's hcl palette Roma as set values on a grid given as a matrix.

par(mar=c(0, 0, 0, 0))
image(image_matrix[350:1600, 1:1250], 
      col=hcl.colors(2000,  palette="Roma"),
      axes=FALSE, useRaster=TRUE)

And an other zooming

par(mar=c(0, 0, 0, 0))
image(image_matrix[800:1200, 200:600], 
      col=hcl.colors(2000,  palette="Roma"),
      axes=FALSE, useRaster=TRUE)

Acknowledgements

Author is grateful to Ranjan Maitra for his suggestions on reviving the package.