Biomedical Engineering Reference
In-Depth Information
Fig. 3 Eden, Biomorph model, Karl Sims genetic image, William Latham
'
s 3D form
2.1 Algorithms to Visualize Arti
cial Life
Cellular automata is a discrete model used in the
eld of computer science to model
von Neumann (self-reproducing) comprising of a grid of squares where each square
is termed to be a cell. Each cell has a state which is interpreted using rules which
relatively evolve the cell to illustrate complex behavior and form structures. The set
of neighboring cells, states, color pallets, and the rules de
ned to model the
environment play a major role in effecting the behavior of the automaton. It makes a
great initial model to build a system of many objects with varying states over time.
Most important detail of how cellular automata works relates to time. Time does not
refer to real-world time, but it is about cells on a grid living over a period of time
called as the
s
neighborhood at the previous generation which mathematically is represented as
[
13
]
“
generation.
”
The cell
'
s new state is a function of the entire cell
'
CELL state at time t
¼
f
ð
CELL neighborhood at time t
1
Þ
:
The edge cells of a grid remain constant, wrap around, or have different
neighborhoods with different rule sets all together. Different rule sets produce
different and complex patterns which vary from generation to generation [
13
].
Excluding traditional cellular automata, various other variations can also be used
for modeling. Non-rectangular grids can be used, cellular automata can be proba-
bilistic in nature where exact outcome need not be de
ned previously, and it can be
continuous where the order of state values can range from 0 to 1, allowing the use
of
16
].
Image processing algorithms operate on cellular automata like rules where opera-
tion performed on a pixel has direct effect on the neighboring pixels. Cellular
automata can also relate to idea of complex adaptive system and be historic in
nature where the current and the previous states of a cell are to be tracked. Cells
rather than having a
fl
oating-point values for the state as used in hodgepodge algorithm [
14
-
xed position on a grid can be implemented as movable such
that cells move about the screen freely without sticking to a
xed position. Systems
can also be made nested to make modeling effective; for example, organ is a
complex system of cells [
13
].
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