There are many patterns and much regularity in a Sierpinski Gasket. Encourage students to describe the patterns and regularity that they see. Write down what they say. Help them examine the words that they use so that they are satisfied with the accuracy and precision of their description.
Most students are familiar with patterns that involve repitition and balance.
The Sierpinski gasket has another property which is quite common in nature, but not always noticed. This property is called self-similarity . The Sierpinski Gasket is self-similar because small parts of it, when magnified, are actually replicas of the whole thing. That is the sense in which it is similar to itself. You will see that a coastline, a fern leaf, the outline of a mountain, and a head of broccoli, if you look at them carefully, are all self-similar.