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by Drew O.
When I learned about fractals in high school math class, I immediately
found
them fascinating. For those of you unfamiliar with the concept, the
definition
from Wikipedia is as follows: a fractal is “a rough or fragmented
geometric
shape that can be subdivided in parts, each of which is (at least
approximately)
a reduced-size copy of the whole”.
At the end of the unit in which we were taught them, the fractal below
was a
test question. In subsequent years, I began drawing it freehand to
higher and
higher levels. The details and patterns that emerge are fascinating.
The goal is to create a ruby program which takes the level as an
argument and
then draws the fractal shown below to the specified level. The fractal
is
created by drawing the first level, then repeating the pattern such that
each
base piece is replaced with the fractal from the higher level. Thus, to
move
from level 1 to level 2, we replace each line with the shape at level 1.
Notice
that the position changes as well, meaning if the line is vertical we
replace it
with a vertically positioned shape of level 1 (right and left facing
also
matter). I have shown the first 3 levels below (including the base
component at
level 0). Feel free to use the console for output or get fancy with
RMagick or
something similar.
_ <-- Level 0
_
_| |_ <-- Level 1
_
_| |_
_| |_ <-- Level 2
_|_ _|_
_| |_| |_| |_
_
_| |_
_| |_
_|_ _|_
_| |_| |_| |_
_| |_
_|_ _|_
_| |_| |_| |_ <-- Level 3
_| |_
_|_ _|_
_| |_|_ _ _ _|_| |_
_| |_|_|_| |_|_|_| |_
_|_ _|_|_ _|_|_ _|_
| || || || || || || |