
Recent Posts
Recent Comments
Archives
 December 2017
 November 2017
 September 2017
 August 2017
 July 2017
 June 2017
 May 2017
 February 2017
 January 2017
 November 2016
 February 2014
 January 2014
 December 2013
 November 2013
 October 2013
 September 2013
 August 2013
 May 2013
 April 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
 July 2012
 June 2012
 May 2012
 April 2012
Categories
Meta
Monthly Archives: October 2013
Coloring the Julia set
The Julia set of a function f(z) in the complex plane has all points z that remain finite upon iterations of the function. In the last posts I have used expanding functions to get fractal images from iteration, as discussed … Continue reading
Posted in Fractals, Selfsimilarity, Uncategorized
Tagged fractal, Iterated function, iteration, julia set, Rotational symmetry, Selfsimilarity
Leave a comment
Rainbow colors
We can define a continuous number x of iterations needed to reach the critical radius R. Note that if the nth iteration of f(z) equals R then x=n, and if the (n1)th iteration equals R then x=n1. For values inbetween … Continue reading
Posted in Fractals, programming, Selfsimilarity
Tagged Color, fractal, fractal design, Rotational symmetry
Leave a comment
Hints for experiments
You can modify the code of the last post “selfsimilar fractals … – the code” to produce new images. A large value for the imaginary part of the constant c often destroys the mirror symmetry and gives a more dynamic … Continue reading
Posted in Fractals, programming
Tagged fractal, fractal design, Rotational symmetry, Selfsimilarity
Leave a comment
selfsimilar fractals from function iteration – the code
// this reproduces the image of ” selfsimilar fractals with …” // you can make your own experiments, try the codes hidden as comments // this is for the main tab of processing // it needs the code of “from … Continue reading
Posted in Fractals, programming
Tagged fractal, fractal design, processing, programming
Leave a comment
From pixels to coordinates – with code
This is similar to “setting up the coordinates” but goes in opposite direction. We now know the coordinates (i,j) of a pixel on the screen and we need to know the corresponding coordinates (x,y) in the complex plane. We want … Continue reading
Posted in Uncategorized
Leave a comment
complex numbers – the code
// see the last post “using complex numbers” for more details class Complex{ float x,y; Complex(float xp,float yp){ x=xp; y=yp; } // addition Complex add(Complex two){ return new Complex(x+two.x,y+two.y); } … Continue reading
Using complex numbers
For complex functions f(z) needed to create fractals we could calculate the real and imaginary part separately using basic arithmetic with float numbers. But this is hard to do and may cause many programming errors. It is better to use … Continue reading
Posted in programming
Tagged complex arithmetic, complex numbers, object oriented programming, programming
Leave a comment