Coloring Pascal's Triangle
It
turns out that Pascal's triangle holds many interesting numeric patterns. One
way of seeing some of these patterns is to pick a number x and color all
numbers in the triangle that are evenly divisible by x with one color,
and all the other numbers in the triangle with a second color. To see as much of
the pattern as possible, you need to be able to see as many rows of the triangle
as possible, but coloring a large number of rows like this by hand is very
boring and time consuming. A computer can color 128 rows of the triangle in only
a few seconds. http://www.cs.washington.edu/homes/jbaer/classes/blaise/blaise.html
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When
all the odd numbers (numbers not divisible by 2) in Pascal's Triangle are
filled in (black) and the rest (the evens) are left blank (white), the
recursive Sierpinski Triangle fractal is revealed (see figure at near
right), showing yet another pattern in Pascal's Triangle. Other
interesting patterns are formed if the elements not divisible by other
numbers are filled, especially those indivisible by prime numbers |