Patterns in nature result from dynamic relationships of forces and constraints. What is analogous for patterns in art? Art is created by human hands motivated by inspiration and thought. It is the product of creativity and skill. Creativity is constrained by cognitive processes and skill by the limits of technology. Based upon the author’s studies of Oriental carpets, this paper suggests that p...

In [4] an informal algorithm ’to display interesting numeric patterns’ is described without any proof. We generalize this algorithm over arbitrary finite fields of characteristic p and we prove that it really generates self-similar carperts, provided that they contain at least one zero in the first (p+1)/2 lines. For the fields Fp the generalized algorithm produces p− 1 different self-similar c...

We achieve on self-affine Sierpinski carpets the multifractal analysis of the Birkhoff averages of potentials satisfying a Dini condition. Given such a potential, the corresponding Hausdorff spectrum cannot be deduced from that of the associated Gibbs measure by a simple transformation. Indeed, these spectra are respectively obtained as the Legendre transform of two distinct concave differentia...

The propagation by continuous-time quantum walks (CTQWs) on one-dimensional lattices shows structures in the transition probabilities between different sites reminiscent of quantum carpets. For a system with periodic boundary conditions, we calculate the transition probabilities for a CTQW by diagonalizing the transfer matrix and by a Bloch function ansatz. Remarkably, the results obtained for ...

We consider a class of Gibbs measures on self-affine Sierpinski carpets and perform the multifractal analysis of its elements. These deterministic measures are Gibbs measures associated with bundle random dynamical systems defined on probability spaces whose geometrical structure plays a central rôle. A special subclass of these measures is the class of multinomial measures on Sierpinski carpet...

Wool in carpets is formed by proteins, where many side chains are polar and ionisable, enabling wool to function as a polymeric ligand exchanger. This project has successfully bound either hydrated ferric oxide (HFO) nanoparticles (Figure 1) or a copper(II) salt onto waste carpet to form a sorbent material. The strongest binding was seen after first modifying the carpet by an alkaline oxidation...

Oriental carpets have been recognized as prestigious furnishing in the West since the Middle Ages. In many ways, they represent the epitome of Western concern with alien things especially utilitarian alien things. Carpets entered the Western cultural arena as a rare alien item of interest and eventually became a commodity. But commoditization does not adequately explain their continuing success...