JuliaImage {Julia}

Julia Set Generator in a Square Region

Description

'JuliaImage' returns two dimensional array representing escape values from on the square region in complex plane. Escape values (which measures the number of iteration before the lenght of the complex value reaches to 2).

Usage

JuliaImage(imageN, centre, L, C)

Arguments

imageN

Number of pixels to equally space division of one side if the square region.

centre

A complex number that determines the centre of the square region

L

A side length of the square region on the complex plane.

C

Complex coefficient

Details

Julia Set is defined as the set of initial complex values where the z = z^2 +C does not diverge to infinity. C is an arbitrary complex constant that does not change during the iteration by definition.

Value

It returns a 2D array of real values from 0 to 1. The array correspods to image on the complex plane.

Note

Post processing to plot/color mapping of the Julia set for visualisation can be done by using the array generated. See examples to get a png output.

Author(s)

Mehmet Suzen <[e-mail]>

References

Gaston Julia (1918) "Memoire sur l'iteration des fonctions rationnelles," Journal de Mathematiques Pures et Appliquees, vol. 8, pages 47-245.

See Also

MandelImage

Examples

# 
# Generating png of the Julia set
# C is 1 minus the golden ratio
#
  imageN <- 5; # increase this to see images
  centre <- 0.0
  L <- 4.0
  C <- 1i-1.6180339887;# Golden Ratio
  image <- JuliaImage(imageN,centre,L,C);
  #library(png)
  #file <- "julia1.png"
  #writePNG(image,file); # possible visulation
#
#  Generating png of the Julia set
# different coefficient.
#
  imageN <- 5; # increase this to see images
  centre <- 0.0
  L <- 4.0
  C <- -0.70176-0.3842i
  image <- JuliaImage(imageN,centre,L,C);
  #library(png)
  #file <- "julia2.png"
  #writePNG(image,file); # possible visulation