Visual Patterns are a great way to utilize patterns to encourage making use of structure in problem-solving. Students make observations and build on those observations to generalizations.
Visual Patterns is a collection of hundreds of visual patterns gathered by Fawn Nguyen. There are patterns that can be used to explore linear function, quadratic functions, cubic functions,
For some ideas about how to use visual patterns with adult students, including handouts and a lesson plan, read Developing Algebraic Reasoning Through Visual Patterns
Mathigon has a visual pattern tool that can help make students' thinking visible to classmates and teachers.