Try doing both. First make dozen pattern yourself and and random element after that. It's easier that way.
Example.

Now you can multiply those with any random seed.
Example 2.


Now you can multiply this or change the base number.

With that approach I bet you can solve this problem easily.

Ey there

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