The k-fractal of a simplicial complex
نویسندگان
چکیده
The k-polynomial of a simplicial complex C is the function kC(x)= ∑ i¿1 fix i where fi is the number of i-faces in C. These k-polynomials are closed under composition, and we are lead to ask: for higher composites of a complex C with itself, what happens to the roots of their k-polynomials? We prove that they converge to the Julia set of kC(x), thereby associating with C a fractal. For 2-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. c © 2003 Elsevier B.V. All rights reserved.
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عنوان ژورنال:
- Discrete Mathematics
دوره 285 شماره
صفحات -
تاریخ انتشار 2004