# Exercises for Chaos Under Control

## Chapter 3: Simplicity and Complexity in Classical Geometry

1. Euclidean description of a right isosceles gasket.

(a) Write the equations for the three lines defining the outer edge
of the gasket with corners (0,0), (0,1), and (1,0).

(b) Write the equations for the three new lines involved in the first
stage of the construction of this gasket. (That is, in removing the
middle triangle.)

(c) How many new lines are needed for the second stage of the gasket?

(d) How many new lines are needed for the third stage of the gasket?

(e) How many equations would be needed to describe the gasket in this
fashion? We call this a **static** description of the gasket, since it
focuses on the appearance as a finished object, not on the dynamical
process by which it is "grown."

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