One day on youtube there was a video which name contains Chaos Game, and my love of superior math was amazed by the video.

Processes mentioned on video:

1. Draw a shape.
2. Pick a random point from the inside of the shape
3. Pick a random corner and put a dot at the midpoint of these two points.
4. Do the 3rd process for the new dot.

When writing these operations to the code, we need to define certain algorithms.

• How do we understand the random point was in the shape?
• When our shape has 4 or more corners, we need to dismiss some corners.* How?

First of all, I use the turtle module for the graphical interface.
It's really simple and I can draw shapes by just use some coordinates.

To pick a random point from inside of the shape, I use that algorithm:

If we draw triangles with a random point and 2 corners, the area of triangles must be equal to the area of the shape.
Nor the point isn't inside of the shape.

1+2+3+4 == Area of Squere

Then we chose a random corner and find the midpoint between the corner and the point.
That is the easiest part of the code. Because has a simple math formula.
And when we put dots to midpoints, the script must be finished.

After a while of this progression, I got shapes like these.

That algorithm is perfectly run at the triangle, but if the shape has 4 or more corners we'll see a miscorrect pattern.

You can change the pattern by changing the corner order.
If we chose a different corner from the last process there won't appear a misspattern. (Example 2nd )
Or you can dismiss the next corner (Example 3rd) or the next 2nd corner (Example 4th).