1. Abelson and diSessa, Turtle Geometry, MIT Press, 1992 2. Erdely, D. http://www.bridgesmathart.org/art exhibits/bridges2007/erdely.html. 3. Gangopadhyay, T. On an alternate construction method for generating spidrons and new tiling patterns generated by them, International journal of Computer Applications, Volume 160, number 3, 2017. 4. Gangopadhyay, T. On subdividing regular polygons using s...

We present a detailed calculation of the recently published exact solution of a random tiling model possessing an eight-fold symmetric phase. The solution is obtained using Bethe Ansatz and provides closed expressions for the entropy and phason elastic constants. Qualitatively, this model has the same features as the square-triangle random tiling model. We use the method of P. Kalugin, who solv...

A Penrose tiling is a nonperiodic tiling generated by an aperiodic set of prototiles named after Roger Penrose, who investigated these sets in the 1970s. Because all tilings obtained with the Penrose tiles are non-periodic, Penrose tilings are considered aperiodic tilings.[1] Among the infinitely many possible tilings there are two that possess both mirror symmetry and fivefold rotational symme...

Sequence similarity algorithms are used to reconstruct increasing large evolutionary trees involving increasingly distant evolutionary relationships. This paper proposes two sequence similarity algorithms, called the Greedy Tiling and the Random Tiling algorithms, that are both based on the idea of tiling one sequence by parts of another sequence. Experimental comparisons show that the new algo...

A family of n-dimensional Lee spheres L is a tiling of Rn , if ∪L = Rn and for every Lu , Lv ∈ L, the intersection Lu ∩ Lv is contained in the boundary of Lu . If neighboring Lee spheres meet along entire (n−1)-dimensional faces, then L is called a face-to-face tiling. We prove the nonexistence of a face-to-face tiling of R4 with Lee spheres of different radii. c © 2005 Elsevier Ltd. All rights...

In this paper, we define new kinds of Fibonacci numbers, which generalize both Fibonacci, Jacobsthal, Narayana numbers and p-numbers in the distance sense, using definition a between by recurrence relation according to parameter k. Tiling combinatorial interpretations these are presented, explicit formulas that allow us calculate nth number given. Also, their generating functions obtained sums ...