Projekt 4. - Institut for Matematik og Datalogi - Syddansk Universitet

N a t u r v i d e n s k a b e l i g t P r o j e k t / F a r m a c e u t : V a l g f r i t P r o j e k t
Projekt 58. Simulation with Cellular Automata
Vejleder: Daniel Merkle, daniel@imada.sdu.dk
Institut: Institut for Matematik og Datalogi (IMADA)
Praktisk del: Programmering
Gruppeplacering: Biblioteket
Gruppestørrelse: Mindst 3 og max 5 deltagere. Én gruppe kan arbejde med projektet.
Kommentarer: Projektet er sœrligt velegnet til studieordning i datalogi / The project is specially
suitable for students with curriculum in computer science
Keywords:
Computer Science, Cellular Automata, Modeling and Simulation, Pattern
Formation
Abstract
In 1952 the English mathematician, logician,
and computer scientist Alan Turing stated: “It
is suggested that a system of chemical substances,
called morphogens, reacting together
and diffusing through a tissue, is adequate to
account for the main phenomena of morphogenesis.''
With relatively easy mathematical
formulations and by means of simulations
with so-called cellular automata (CA), it is
possible to model and analyze the related problem of pattern formation that occurs on sea shells
or on animal skins. A CA is a remarkable simple discrete model studied in computability theory
that consists of a regular grid of cells each in one of a finite number of states, such as “On” and
“Off”. Each cell has a finite set of neighborhood cells. The current state of a cell itself and the
current states of the cells in its neighborhood are considered to determine synchronously the new
state of a cell.
In a straightforward manner such CA can be used to simulate the mechanism that is supposed to
be responsible for generating the before mentioned patterns. This mechanism is based on a socalled
reaction-diffusion system of the morphogen prepatterns. The subsequent differentiation of
cells to produce melanin (pigments that affect skin color) simply reflects the spatial patterns of
morphogen concentration.
An introduction to cellular automata will be included. The project aims at giving the participants
knowledge on modeling with CA and experience in the implementation of CA-based simulations
(simulation of animal skin patterns is just one suggestion).
Minikurser
Obligatorisk: Projektarbejde (LaTeX).
Anbefalede: Ingen
Litteraturliste over metode artikler, som udleveres til de studerende
A. Deutsch, S. Dormann: Cellular Automaton Modeling of Biological Pattern Formation,
Birkhäuser Boston, 2005.
L.B. Kier, P.G. Seybold, and C.-K. Cheng: Modeling Chemical Systems Using Cellular Automata,
Springer Netherlands, pages 9-38, 2005.
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