space-filling curves have interested mathematicians for centurie

Project Description:

space-filling curves have interested mathematicians for centuries. in the limit, these curves have infinite length, but they are confined to a finite rectangle and never cross themselves. many of these curves can be generated iteratively. consider the "rule" pictured in figure 2.48 that replaces a single line segment with four shorter segments. write a program that starts with a triangle and iteratively applies the replacement rule to all the line segments. the object that you generate is called the koch snowflake. for other examples of space-filling curves, see [hil07] and [bar93].
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