What is this pattern/tile board game?
It very much reminds me of a pentomino puzzle. Square board where you try to build certain shapes. I believe Tangram is a pentomino puzzle variant. Linked is an example of what I'm talking about (pieces are made of wood but you get the idea).

https://www.amazon.com/Square-Root-00012-Pentominoes/dp/B00000IZUL

Good luck finding your game!