Abstract
We consider Pascal’s Triangle [Formula: see text] to be the entries of Pascal’s Triangle that are congruent to [Formula: see text]. Such a representation of Pascal’s Triangle exhibits fractal-like structures. When the Triangle is mapped to a subset of the unit square, we show that such a set is nonempty and exists as a limit of a sequence of coarse approximations. We then show that for any given prime [Formula: see text], any such sequence converges to the same set, regardless of the residue(s) considered. As an obvious consequence, this allows us to conclude that the fractal (box-counting) dimension of this nonempty, compact representation of Pascal’s Triangle [Formula: see text] is independent of [Formula: see text].
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