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1. INTRODUCTION. For more than twenty years, fractals have intrigued mathematicians and nonmathematicians alike due to their inherent beauty and widespread appearance in nature and computer graphics. Intuitively, a fractal is a geometric object with intricate detail on an arbitrarily small scale and some measure of self-similarity. Formally, a fractal is a… (More)

In this paper, we give necessary and sufficient conditions that determine when a vertex replacement rule given by exactly one replacement graph generates an infinite graph with exponential growth and when it generates an infinite graph with polynomial growth. We also compute the formula for the growth degree of infinite graphs with polynomial growth that… (More)

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