Chaotic Fractal Tree
Insructions:
Applet draws nth iteration of fractal tree.
You can set following parameters:
angle - angle of new branch (you can set different values for left and right branches), it should be in the range from 0 to 90.
lenght ratio - lenght of new branch to old barnch (you can set different values for left and right branches), it should be in the range from 0 to 1.
position - position of new branch if it is 1 it corresponds to the end of old branch, when it is 0, it is the beginning of the old branch (you can set different values for left and right branches), it should be in the range from 0 to 1.
percent of chaos - value in percent of random variable that will contribute to values of angle, position and lenght ratio. You can switch on and off random variable for angle, position and lenght ratio.
You need to press Draw button to see changes.
Description:
The fractal tree is constructed by adding to each line segment two others line segments that are shorter. Creating fractal tree you can define the length ratio between subsequent line segments, angle between them and position of new line segments.
You can observe a process of creation of the fractal tree "step by step" setting up step number to one and incrementing it using "+" button.
Percent of chaos is the percent of contribution of random variable in value of angle, position and lenght ratio. It is calculated in following way:
valuenew = (1-A).valueold + A.R
where:
A - is percent of chaos
R - is a random variable, 0 < R < value
Some interesting trees can be drawn by setting position to 0.
If you set angle to 90 you will get something similar to Hilbert curve.
Another interesting tree can be drawn by setting position to 1 and angle to 90 .
Increasing percent of chaos you can observe degeneration of regular tree into something chaotic.
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