1. The <f>k</f>-fractal of a simplicial complex
- Author
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Brown, J.I., Hickman, C.A., and Nowakowski, R.J.
- Subjects
- *
POLYNOMIALS , *MATHEMATICAL functions , *APPROXIMATION theory , *COMPLEX numbers - Abstract
The
k -polynomial of a simplicial complexC is the functionkC(x)=∑i⩾1 fixi wherefi is the number ofi -faces inC . Thesek -polynomials are closed under composition, and we are lead to ask: for higher composites of a complexC with itself, what happens to the roots of theirk -polynomials? We prove that they converge to the Julia set ofkC(x) , thereby associating withC a fractal. For2 -dimensional complexes we exploit the Mandelbrot set to determine when their fractals are connected, and determine the connectness of the fractals for certain families of ‘stripped’ complexes. [Copyright &y& Elsevier]- Published
- 2004
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