1) I recognize a pattern in the way she talks.
In this case,pattern means the regular way in which sth happens or is done .（模式/方式）
For example, patterns of behavior/work/weather (行为/工作/天气的模式)
2) I see the same pattern repeat many times.
You know ,you need to give us a context.
In this case, pattern means a regular arrangement of lines,shapes,colours,etc.
as a design on material ,carpets ,etc.(图案/花样)
It can also mean the regular way in which sth happens or is done .（模式/方式）
3) Just copy this design pattern so we can have matching outfits
In this situation, pattern means a design ,set of instructions or shape to cut around that you use in order to make sth.(图样/模型/底样)
4) I figured out the math problem when I saw the pattern。
Here, pattern means a regular arrangement of lines,shapes,colours,etc (图案)