Overview
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.
Instructions
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!
Variables
| 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). |