Looking at Chaos |

Written by Mike James | |||

Saturday, 05 September 2009 | |||

Page 1 of 2
An article in Babbage's Bag is all about chaos and this seems like a good time to have some fun plotting some chaos diagrams and using the scrolling technique described in the recent project Stripchart Scrolling. The basic idea is very simple. The iteration
is performed to see what values of The values of a that are of interest are between about 2.95 and 4.00. For this range the iteration stays within the interval 0 to 1 and chaos sets in at about When the iteration is started it takes some time to settle down and then it cycles though a finite number of values. The values that the iteration cycles though form the attracting set of the process and it’s these we need to plot. Start a new C# project and place a button and a picturebox on the form.
The button’s click routine does the work of plotting. First we need to make the pictureBox have a persistent drawing surface in the form of a bitmap: private void button1_Click(Next we work out a scaling that gives the correct range of values for to cover the entire picturebox: Double a; We then initialise Double x = 0.2; The next 500 iterations are used to find out what values of for ( int i= 1; i < 500; i++) Finally we Refresh the pictureBox and make sure to dispose of the Graphics object: pictureBox1.Refresh(); If you run this finished program you will see the bifurcation diagram for the map - see the next page. <ASIN:0738204536> <ASIN:0387202293> <ASIN:0821801376> <ASIN:1559533560> |
|||

Last Updated ( Saturday, 05 September 2009 ) |