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Fractals Applet

If your browser could display Java applets, you would see a fractals applet.


This program is a tool to draw geometric forms called fractals.

A fractal has the same structure no matter how far you zoom in.
For example, a tree has branches, each branch has branches, and so on.
If the number of branchings were infinite, the tree would be a true fractal.


Change the number of iterations a few times.
If iterations = 0, you will see a polygon.
If iterations = 1, each side of the polygon is replaced by line segments.
If iterations = 2, each segment is replaced by more segments, and so on.
If iterations = infinity, the pattern is a true fractal.
Usually about 5 iterations is a good approximation.

Experiment with the other controls to see how they work.

To create your own function, it is best to set iterations = 1 and sides = 1
before changing the points, x and y values.
The number of different patterns you can create is very large!


Function A mathematical function to divide a line segment into several smaller segments.
Sides The number of sides of the polygon. If sides = 1 or 2, the shape is instead a line.
Iterations The number of times each line segment in the polygon is divided
(infinite in a true fractal)
Zoom Get closer or farther from the picture (1 is normal).
Amplify Increase or decrease the y values of the function.
Compress Move the x values closer or farther from the center of the function (x=0.5).
Fixed Color The color to draw lines if the color scheme uses only one fixed color.
Color Scheme The method used to color the image.
Draw Mode Whether to draw lines, boxes or filled boxes.
Center Amplify so the highest y value is at the center of the polygon.
Negate Make the y values of the function negative.
Mirror Reflect the x values about the center of the function (x=0.5).
All iterations Draw all steps in the process of creating the fractal.
Random Make a random change to one of the variables.
Redraw Refresh the image in case it was somehow messed up.
Reset Return all variables to their starting values.
Points The number of points in the function.
x1 through y7 The x and y values of the sub-segments in the function.
The endpoints of the segment are (x0, y0) = (0, 0) and (xp+1, yp+1) = (1, 0).