Here are a few examples of how my daughter is learning about patterns while we play.
She loves her wooden threading beads. It is one of things that I will find her playing with quietly in her room in the mornings. Picture 1- She does her own pattern play without any suggestions. Picture 2- I set up some easy patterns for her to complete.
I bought these cubes to practice counting and math skills but they are also great for pattern play. I start a pattern and she will keep going until she runs out of the right color cubes. She has also started trying to make patterns for me to complete. They are not "patterns" yet but it is great to see her trying to learn how to come up with them on her own.
These are magnetic mosaic tiles so they are great to use on our big board or on a cookie sheet on the go. I create simple patterns and she works them until she runs out of tiles. She really likes when I create patterns that allow her to use all the tiles. (Sorry about glare)