in this paper, our purpose is twofold. firstly, the tensor andresiduum operations on $l-$nested systems are introduced under thecondition of complete residuated lattice. then we show that$l-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. thus the new representation theorem of$l-$subsets on complete re...

This material introduces extensions to the graphical interpretation of L-systems based on turtle geometry, resulting in a higher degree of realism of visualized models.

This paper investigates the L-stability properties of fractional nonlinear differential equations. Systems defined on a finite time interval are considered. The principal contributions are summarized in a theorem which give sufficient conditions for bounded stability of fractional order systems. We show that the proposed results can not be extended to the case of systems defined on an infinite ...

The main focus of this paper is the analysis of modern methods of algorithmic plant generation. First, a brief introduction is given to the necessary formalism: Lindenmayer system. It is followed by a description of each stage of plant generation process. These include algorithms for obtaining: leaf venation graph, leaf texture, stem texture, and the geometry and topology of the whole plant. In...

Developmental processes in nature may involve complex changes in the topology, shape, and patterns of growing structures. Processes taking place in one or two dimensions can be visualized as objects in three-dimensional space, obtained by extruding the growing structures along a line or curve representing the progress of time. In this paper, we extend the notion of L-systems with turtle interpr...

Much of music structure might appropriately be viewed as auralized mathematics. African and African Diasporic music traditions are areas of untapped potential for exploring this notion, particularly with respect to the ways in which the elements of pulse, cycle, and subpulse are manipulated in complex rhythmic structures. In this paper, we describe our preliminary investigations into the use of...

The notion of multidimensional quadrilateral lattice is introduced. It is shown that such a lattice is characterized by a system of integrable discrete nonlinear equations. Different useful formulations of the system are given. The geometric construction of the lattice is also discussed and, in particular, it is clarified the number of initial–boundary data which define the lattice uniquely.

M-rate 0L systems are interactionless Lindenmayer systems together with a function assigning to every string a set of multisets of productions that may be applied simultaneously to the string. Also tabled and extended variants of M-rate 0L systems are considered. Some results concerning the computational power of these systems are presented supplementing those contained in [1].