that change over time based on previous characteristics and the characteristics of
individuals with which it interacts. Typically, individuals are represented as cells in
a grid. The features of each cell are determined by its features in the past and those
of the neighboring cells.
The model of this chapter is set up for 100 cells arranged in a square. It is an
extremely simple cellular automaton which has been developed by the British
mathematician John H. Conway. Conway [4] called this model “Life,” perhaps
because the displays of the model looks remarkably like a Petri dish full of
microscopic organisms, moving back and forth, merging with each other, replicating themselves or generating new forms.
The rules for the game of life are as follows:
1. Each cell on the grid can only take on two characteristics, for example, the colors
black or white.
2. If, for a given cell, the number of neighbors is exactly two, the value of the
square does not change at the next time step.
3. If the number of black neighbors is exactly three, the square will be black in the
next time step.
4. If the number of black neighbors is neither two nor three, the square will be
white at the next time step.
We have named the cells in our model with letters A, B, . . ., J for rows and
numbers 1, 2, . . ., 10 for columns. The state of each cell is captured by a state
variable that either takes on a value of one if it is black or zero if it is white. Changes
in the state of a cell are captured by bi-flows and calculated on the basis of its own
state and the value its neighbors take on. If a cell is black (i.e., its state variable
takes on a value of one) and if exactly three of its neighbors are black (the sum of
the state variables of all neighbors is three), then—according to the third rule
above—there is no change in the state of the cell and the bi-flow is zero. If
the cell is white but exactly three of its neighbors are black, then—according to
the third rule above—the bi-flow takes on a value of one, changing the state of the
respective cell from zero to one. Rules two and four can be accommodated
analogously in the model. An example for the application of these rules to one of
the cells in the model is given in the module of Fig. 43.1.
The parameter BIRTH # is the number of neighbor cells that must be black to
“give birth” to a cell. According to our rules we set BIRTH # ¼ 3. Similarly,
NEIGHBOR MAX is the number of cells being black above which the cell dies
from crowding, and NEIGHBOR MIN is the minimum number of neighboring cells
below which the cell is no longer viable. NEIGHBOR MAX and NEIGHBOR MIN
in our model are set to 3 and 2, respectively. The rule for the change in cell B4 is
shown in Eq. (43.1).
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43 Game of Life
individuals with which it interacts. Typically, individuals are represented as cells in
a grid. The features of each cell are determined by its features in the past and those
of the neighboring cells.
The model of this chapter is set up for 100 cells arranged in a square. It is an
extremely simple cellular automaton which has been developed by the British
mathematician John H. Conway. Conway [4] called this model “Life,” perhaps
because the displays of the model looks remarkably like a Petri dish full of
microscopic organisms, moving back and forth, merging with each other, replicating themselves or generating new forms.
The rules for the game of life are as follows:
1. Each cell on the grid can only take on two characteristics, for example, the colors
black or white.
2. If, for a given cell, the number of neighbors is exactly two, the value of the
square does not change at the next time step.
3. If the number of black neighbors is exactly three, the square will be black in the
next time step.
4. If the number of black neighbors is neither two nor three, the square will be
white at the next time step.
We have named the cells in our model with letters A, B, . . ., J for rows and
numbers 1, 2, . . ., 10 for columns. The state of each cell is captured by a state
variable that either takes on a value of one if it is black or zero if it is white. Changes
in the state of a cell are captured by bi-flows and calculated on the basis of its own
state and the value its neighbors take on. If a cell is black (i.e., its state variable
takes on a value of one) and if exactly three of its neighbors are black (the sum of
the state variables of all neighbors is three), then—according to the third rule
above—there is no change in the state of the cell and the bi-flow is zero. If
the cell is white but exactly three of its neighbors are black, then—according to
the third rule above—the bi-flow takes on a value of one, changing the state of the
respective cell from zero to one. Rules two and four can be accommodated
analogously in the model. An example for the application of these rules to one of
the cells in the model is given in the module of Fig. 43.1.
The parameter BIRTH # is the number of neighbor cells that must be black to
“give birth” to a cell. According to our rules we set BIRTH # ¼ 3. Similarly,
NEIGHBOR MAX is the number of cells being black above which the cell dies
from crowding, and NEIGHBOR MIN is the minimum number of neighboring cells
below which the cell is no longer viable. NEIGHBOR MAX and NEIGHBOR MIN
in our model are set to 3 and 2, respectively. The rule for the change in cell B4 is
shown in Eq. (43.1).
392
43 Game of Life