Hanoi attractors and the Sierpiński gasket
نویسندگان
چکیده
The famous game Towers of Hanoi is related with a family of so–called Hanoi–graphs. We regard these non self–similar graphs as geometrical objects and obtain a sequence of fractals (HGα)α converging to the Sierpiński gasket which is one of the best studied fractals. It is shown that this convergence holds not only with respect to the Hausdorff distance, but that also Hausdorff dimension does converge. Moreover, it is shown that each of the approximating sets has nontrivial Hausdorff measure.
منابع مشابه
Coloring Sierpiński graphs and Sierpiński gasket graphs
Sierpiński graphs S(n, 3) are the graphs of the Tower of Hanoi with n disks, while Sierpiński gasket graphs Sn are the graphs naturally defined by the finite number of iterations that lead to the Sierpiński gasket. An explicit labeling of the vertices of Sn is introduced. It is proved that Sn is uniquely 3-colorable, that S(n, 3) is uniquely 3-edgecolorable, and that χ′(Sn) = 4, thus answering ...
متن کاملWeighted Spanning Trees on some Self-Similar Graphs
We compute the complexity of two infinite families of finite graphs: the Sierpiński graphs, which are finite approximations of the well-known Sierpiński gasket, and the Schreier graphs of the Hanoi Towers group H(3) acting on the rooted ternary tree. For both of them, we study the weighted generating functions of the spanning trees, associated with several natural labellings of the edge sets.
متن کاملOn the Hausdorff Dimension of the Sierpiński Gasket with respect to the Harmonic Metric
The spectral dimension and the Hausdorff dimension of the Sierpiński gasket are known to be different. Kigami proved that the Hausdorff dimension dh with respect to the harmonic metric is less than or equal to the spectral dimension and conjectured equality. We give estimates of dh which are strictly less than the spectral dimension and therefore disprove this conjecture. 1. Sierpiński gasket a...
متن کاملThe anisotropic quantum antiferromagnet on the Sierpiński gasket: Ground state and thermodynamics
We investigate an antiferromagnetic s=1/2 quantum spin system with anisotropic spin exchange on a fractal lattice, the Sierpiński gasket. We introduce a novel approximative numerical method, the configuration selective diagonalization (CSD) and apply this method to a the Sierpiński gasket with N=42. Using this and other methods we calculate ground state energies, spin gap, spin–spin correlation...
متن کاملRandom Walks on Sierpiński Graphs: Hyperbolicity and Stochastic Homogenization
We introduce two new techniques to the analysis on fractals. One is based on the presentation of the fractal as the boundary of a countable Gromov hyperbolic graph, whereas the other one consists in taking all possible “backward” extensions of the above hyperbolic graph and considering them as the classes of a discrete equivalence relation on an appropriate compact space. Illustrating these tec...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- IJMNO
دوره 3 شماره
صفحات -
تاریخ انتشار 2012