These images are based on simple points. This post explains how it works.
1. Step: Point, points, points …
The starting point is a rectangle a grid that is populated with many thousand points, in this case 3,969.
The retangle is placed in a coordinate system, so every point has two coordinates (x, y).
2. Step:
Now, the position of every single points is transformed. This new position is calculated by a formula, which has random parameters. Because of the random numbers, every image looks different.
For example, using a combination of sine, cosine and the random factor:
Circle resembling shapes are created by using a polar coordinate system:
Do it yourself
I wrote a package called generativeart which helps to create those kind of images with R.
You can get the package on Github.