I figured I could help when I attempted to make a game very similar to this a while back.
If you would like the patterns to be completely randomized, you may create a method(or a few) to generate a pattern by means of a Random generator.
In a simple way, you may create a line to represent your pattern. The game I had was a lame attempt at a 4k game, where 5 circles were shown , and the 6th had to be guessed by the player.
There are 2 main things to take into consideration: how often your pattern will tesselate(or repeat) and how the data is selected to be shown(which colors to show).
By looking into this, you can code yourself a genertor for a random tesselation number and random numbers to represent an image to show.
Understand what I'm getting to?
Hope I helped a bit