MGF 1107 – EXPLORATIONS IN MATHEMATICS
LECTURE 30
The Koch Antisnowflake
In the previous lecture we looked at how to construct the Koch
snowflake starting with an equilateral triangle. A variation on this is the
Koch antisnowflake
, where instead of the middle third of each side
being replaced by two sides of an equilateral triangle whose vertex
points away from the center of the triangle (thereby increasing the area),
we replace the middle third of each side and delete an area formed by
two sides of an equilateral triangle whose vertex points towards the
center of the triangle (thus decreasing the area).
Ex.
Assume that the Koch antisnowflake starts with sides of length 1.
Let M denotes the number of sides, l the length of each side, and P the
perimeter. Then we can construct the following table:
Iteration
M
l
P
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
The Sierpinski Triangle
Another famous fractal is the Sierpinski triangle, created by Wac
ł
aw
Sierpi
ń
ski (18821969). We start with an equilateral triangle and split it
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 EVINSON
 Math, Calculus, Fractal Geometry, Fractal, sierpinski triangle

Click to edit the document details