357 research outputs found
L-systems in Geometric Modeling
We show that parametric context-sensitive L-systems with affine geometry
interpretation provide a succinct description of some of the most fundamental
algorithms of geometric modeling of curves. Examples include the
Lane-Riesenfeld algorithm for generating B-splines, the de Casteljau algorithm
for generating Bezier curves, and their extensions to rational curves. Our
results generalize the previously reported geometric-modeling applications of
L-systems, which were limited to subdivision curves.Comment: In Proceedings DCFS 2010, arXiv:1008.127
Leonardo's rule, self-similarity and wind-induced stresses in trees
Examining botanical trees, Leonardo da Vinci noted that the total
cross-section of branches is conserved across branching nodes. In this Letter,
it is proposed that this rule is a consequence of the tree skeleton having a
self-similar structure and the branch diameters being adjusted to resist
wind-induced loads
Self-repair ability of evolved self-assembling systems in cellular automata
Self-repairing systems are those that are able to reconfigure themselves following disruptions to bring them back into a defined normal state. In this paper we explore the self-repair ability of some cellular automata-like systems, which differ from classical cellular automata by the introduction of a local diffusion process inspired by chemical signalling processes in biological development. The update rules in these systems are evolved using genetic programming to self-assemble towards a target pattern. In particular, we demonstrate that once the update rules have been evolved for self-assembly, many of those update rules also provide a self-repair ability without any additional evolutionary process aimed specifically at self-repair
A complementary view on the growth of directory trees
Trees are a special sub-class of networks with unique properties, such as the
level distribution which has often been overlooked. We analyse a general tree
growth model proposed by Klemm {\em et. al.} (2005) to explain the growth of
user-generated directory structures in computers. The model has a single
parameter which interpolates between preferential attachment and random
growth. Our analysis results in three contributions: First, we propose a more
efficient estimation method for based on the degree distribution, which is
one specific representation of the model. Next, we introduce the concept of a
level distribution and analytically solve the model for this representation.
This allows for an alternative and independent measure of . We argue that,
to capture real growth processes, the estimations from the degree and the
level distributions should coincide. Thus, we finally apply both
representations to validate the model with synthetically generated tree
structures, as well as with collected data of user directories. In the case of
real directory structures, we show that measured from the level
distribution are incompatible with measured from the degree distribution.
In contrast to this, we find perfect agreement in the case of simulated data.
Thus, we conclude that the model is an incomplete description of the growth of
real directory structures as it fails to reproduce the level distribution. This
insight can be generalised to point out the importance of the level
distribution for modeling tree growth.Comment: 16 pages, 7 figure
Multiscale Bone Remodelling with Spatial P Systems
Many biological phenomena are inherently multiscale, i.e. they are
characterized by interactions involving different spatial and temporal scales
simultaneously. Though several approaches have been proposed to provide
"multilayer" models, only Complex Automata, derived from Cellular Automata,
naturally embed spatial information and realize multiscaling with
well-established inter-scale integration schemas. Spatial P systems, a variant
of P systems in which a more geometric concept of space has been added, have
several characteristics in common with Cellular Automata. We propose such a
formalism as a basis to rephrase the Complex Automata multiscaling approach
and, in this perspective, provide a 2-scale Spatial P system describing bone
remodelling. The proposed model not only results to be highly faithful and
expressive in a multiscale scenario, but also highlights the need of a deep and
formal expressiveness study involving Complex Automata, Spatial P systems and
other promising multiscale approaches, such as our shape-based one already
resulted to be highly faithful.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005
Shall We (Math and) Dance?
Can we use mathematics, and in particular the abstract branch of category
theory, to describe some basics of dance, and to highlight structural
similarities between music and dance? We first summarize recent studies between
mathematics and dance, and between music and categories. Then, we extend this
formalism and diagrammatic thinking style to dance.Comment: preprin
- …