We consider finite point-set approximations of a manifold or fractal with the goal of determining topological properties of the underlying set. We use the minimal spanning tree of the finite set of points to compute the number and size of its -connected components. By extrapolating the limiting behavior of these quantities as → 0 we can say whether the underlying set appears to be connected, to...

We study the scaling properties of the clusters grown by the Wolff algorithm on seven different Sierpinski-type fractals of Hausdorff dimension 1 < df ≤ 3 in the framework of the Ising model. The mean absolute value of the surface energy of Wolff cluster follows a power law with respect to the lattice size. Moreover, we investigate the probability density distribution of the surface energy of W...

This work presents Squeeze, an efficient compact fractal processing scheme for tensor core GPUs. By combining discrete-space transformations between and expanded forms, one can do data-parallel computation on a with neighborhood access without needing to expand the in memory. The space are formulated as two GPU tensor-core accelerated thread maps, ?(?) ?(?), which act compact-to-expanded expand...

Abstract Non-Hermitian (NH) crystals, quasicrystals, and amorphous network display an accumulation of a macroscopic number states near one its specific interfaces with vacuum, such as edge, surface, hinge, or corner. This phenomenon is known the NH skin effect, which can only be observed open boundary condition. In this regard self-similar fractals, manifesting inner boundaries in interior syst...

Obstacles arranged into a pre-fractal shape (Sierpinski carpet) were tested for their blast attenuation abilities using 250 g PE4 at three different scaled distances ( Z = 1.87, 2.24, 2.99 m/kg 1/3 ). Three iterations tested, as well free-field tests comparative purposes. Reductions in peak overpressure up to 26% and specific impulse 19% observed, attributed mechanism known ‘trapping’. This is ...

Let a be a positive real number, a < 1/2. A standard construction of a self-similar Cantor set in the plane starts with the unit square [0, 1]× [0, 1], replaces it with the four corner squares with sidelength a, then replaces each of those squares with their four corner squares of sidelength a, and so on. At the nth stage one has 4 squares with sidelength a, and the resulting Cantor set has Hau...

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by χ′a(G). Sierpinski graphs S(n, 3) are the graphs of the Tower of Hanoi with n disks, while Sierpinski gasket graphs Sn are the graphs naturally defined ...

The Sierpinski triangle also known as Sierpinski gasket is one of the most interesting and the simplest fractal shapes in existence. There are many different and easy ways to generate a Sierpinski triangle. In this paper we have presented a new algorithm for generating the sierpinski gasket using complex variables.

We study here $T_{0}$-$Q$-bitopological spaces and sober $Q$-bitopological spaces and their relationship with two particular Sierpinski objects in the category of $Q$-bitopological spaces. The epireflective hulls of both these Sierpinski objects in the category of $Q$-bitopological spaces turn out to be the category of $T_0$-$Q$-bitopological spaces. We show that only one of these Sierpinski ob...

Explicit determination of the mean first-passage time (MFPT) for trapping problem on complex media is a theoretical challenge. In this paper, we study random walks on the Apollonian network with a trap fixed at a given hub node (i.e. node with the highest degree), which are simultaneously scale-free and small-world. We obtain the precise analytic expression for the MFPT that is confirmed by dir...