On the classification of fractal square dendrites
Keywords:
ractal square, dendrite, self-similar boundary, main tree, ramification pointAbstract
We consider the classification of fractal square dendrites K based on the types of the self-similar boundary ∂K and the main tree γ of such dendrites. We show that the self-similar boundary of a fractal square dendrite K may be of 5 possible types and may consist of 3,4 or 6 points. We prove that the main trees of fractal square dendrites belong to 7 possible classes. Bearing in mind the placement and orders of the points of ∂K with respect to the main tree γ, this results in 16 possible types of main trees for non-degenerate fractal square dendrites.
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