Introduction
In this post I'll shortly describe some functions from a fractals generator that I wrote in Haskell. Some parts of the application are from the repository mentioned in this post. Some modules, like Plots, are reused from that module since I don't have experience with working with images in Haskell.
Currently there are not so much differences between the original repository and what I pushed into my repository but I hope that, in future, after I implement my ideas, the code will look more different.
Regarding the ideas that I have and the fractals generator, maybe this post will start a short series of posts regarding this topic. First of all I want to have a generator that will use threads to draw parts of the fractal, to implement some command line arguments and to switch between a mode that will only save the drawing of a specified fractal and a mode that will permit also zooming.
Implementation
First of all, let's start with a colors' palette. For this project I will start by generating a palette of 4096 colors.
colorPalette::[[Int]]
colorPalette = [[r,g,b] | r<-[0,16..255],g<-[0,16..255],b<-[0,16..255]]
Basically I organize the data as a list of lists. Each inner list contains three values corresponding to RGB. Function getColor defined below returns the selected color based on the current iteration.
getColor::Int -> Color
getColor x
| x > maxNumberOfIterations = rgb 255 255 255
| otherwise = let c = colorPalette !! x
in rgb (c !! 0) (c !! 1) (c !! 2)
Regarding the actual fractal generation, I will present only the function for drawing the Mandelbrot fractal.
mandelbrot::Complex Double
-> Complex Double
-> Int
-> Int
mandelbrot z c iter
| iter > maxNumberOfIterations = 0
| otherwise = let zNext = z^2 + c in
if magnitude zNext > 2
then iter
else mandelbrot zNext c (iter+1)
Without getting too much into details, this function has 3 parameters, z, c and iter, of Complex Double and Int types and returns an Int value. From implementation point of view, if current iteration is greater than the maximum allowed number of iterations, then the function returns 0, otherwise, it will calculate zNext.
Conclusions
No words, only pictures!
