Pattern Machine Coding Tutorial: Bi-Directional122

Introduction

A bi-directional pattern machine is a type of reversible cellular automaton that can be programmed to generate patterns that move in both directions. This makes them ideal for creating complex and dynamic patterns, such as waves, spirals, and fractals. In this tutorial, we'll learn how to program a bi-directional pattern machine using Python.

How a Bi-Directional Pattern Machine Works

A bi-directional pattern machine consists of a grid of cells, each of which can be in one of two states: on or off. The state of each cell is determined by the states of its neighbors in the previous time step. The rules for updating the state of a cell are called the transition rules.

The transition rules for a bi-directional pattern machine are typically defined using a truth table. The truth table specifies the state of a cell in the next time step for all possible combinations of states of its neighbors in the previous time step. For example, the following truth table defines a bi-directional pattern machine that generates a wave pattern:

Neighbor States
Cell State in Next Time Step


000
0


001
1


010
0


011
1


100
1


101
0


110
1


111
0

To use the truth table to update the state of a cell, we simply look up the corresponding row in the table based on the states of the cell's neighbors in the previous time step. For example, if a cell has two neighbors that are on and one neighbor that is off, then the cell's state in the next time step will be on (according to the fourth row of the truth table).

Programming a Bi-Directional Pattern Machine

Now that we understand how a bi-directional pattern machine works, we can learn how to program one using Python. The following Python code defines a class that implements a bi-directional pattern machine:```
class PatternMachine:
def __init__(self, width, height, transition_table):
= width
= height
self.transition_table = transition_table
= [[0 for _ in range(width)] for _ in range(height)]
def update(self):
new_grid = [[0 for _ in range()] for _ in range()]
for i in range():
for j in range():
neighbors = self.get_neighbors(i, j)
new_grid[i][j] = self.transition_table[neighbors]
= new_grid
def get_neighbors(self, i, j):
neighbors = []
for x in range(i-1, i+2):
for y in range(j-1, j+2):
if x >= 0 and x < and y >= 0 and y < :
([x][y])
return neighbors
def print_grid(self):
for row in :
print(' '.join(['*' if cell else ' ' for cell in row]))
```

The `PatternMachine` class has the following attributes:* `width`: The width of the grid.
* `height`: The height of the grid.
* `transition_table`: A dictionary that maps neighbor states to cell states.
* `grid`: A 2D list that represents the state of the grid.

The `PatternMachine` class also has the following methods:* `update()`: Updates the state of the grid based on the transition table.
* `get_neighbors(i, j)`: Returns a list of the states of the neighbors of the cell at position (i, j).
* `print_grid()`: Prints the state of the grid to the console.

Example

The following code shows how to use the `PatternMachine` class to create a bi-directional pattern machine that generates a wave pattern:```
pattern_machine = PatternMachine(10, 10, {
(0, 0, 0): 0,
(0, 0, 1): 1,
(0, 1, 0): 0,
(0, 1, 1): 1,
(1, 0, 0): 1,
(1, 0, 1): 0,
(1, 1, 0): 1,
(1, 1, 1): 0
})
for _ in range(100):
()
pattern_machine.print_grid()
```

The output of the code is a wave pattern that moves across the grid.

Conclusion

Bi-directional pattern machines are a powerful tool for creating complex and dynamic patterns. They are relatively easy to program, and they can be used to create a wide variety of visual effects.

2025-02-17

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