LT Cellular Automata App

Install the LT Cellular Automata app from the Microsoft Store

Features

Main Screen

Automaton Screen / Simulation

Editing Rules

Editing Colors

Changing the Initial Cell Density

Drawing in the Automaton Field

The LT Cellular Automata app generates patterns according to rules specified by the user. Sometimes very simple rules generate patterns of astonishing complexity. The patterns are generated on a two-dimensional lattice of cells. Each cell can be in one of two states: alive (on) or dead (off). A transition between the states is influenced by the eight cells surrounding each cell - the cell's neighbourhood.

Initially, the lattice is populated randomly with alive and dead cells. After starting the simulation, the cells evolve by reproducing, dying, or surviving according to the user-defined rules. These rules are applied simultaneously to all the cells on the lattice.

The LT Cellular Automata app is able to generate smooth transitions wherein each cell can be in up to 100 intermediate stages between alive and dead states. These transitional stages are represented by the shades of the two user-defined colors.

There is also an option of drawing the initial state of the automaton field with a mouse or, on touch devices, with fingers.

The app may be useful for creating seamless tiles. A seamless tile is an image where opposite edges match up when placed side by side.

Features

A set of sample automata including the Conway's Game of Life.
Adding new cellular automata and defining custom rules.
Adjusting simulation parameters: the speed, the cell size, the initial density, etc.
Saving an automaton image as a PNG file.
Simulating smooth transitions with up to 100 intermediate stages between alive and dead states.
Drawing the initial state of the automaton field.
Taking a thumbnail for easy automaton identification.

Main Screen

The main screen displays a list of sample automata. Each automaton has its own thumbnail for easy identification:

You can select an automaton by right-clicking its tile. This enables the Copy and Remove options:

Copy - copies the selected automaton
Remove - deletes the selected automaton
Add New - opens a new screen which allows you to add a new automaton

Automaton Screen / Simulation

You can proceed to simulation by clicking an automaton tile in the main screen. Here, we've selected the Conway's Game of Life:

There are two panels on the automaton screen.

The first panel on the left (the control panel) allows you to:

Change the automaton name.
Start and pause the simulation.
Control simulation speed.
Set the initial density of the cells in the automaton field.
Choose a cell size.

The second panel on the right (the automaton field) shows the progress of simulation graphically.

Six options are available from the automaton screen's menu at the bottom:

Save Changes - saves changes made to the automaton.
Edit Rules - defines transition rules.
Edit Colors - adjusts colors and shades of the graphical representation of the automaton.
Set Thumbnail - changes the automaton's thumbnail.
Save Image - saves the automaton image to a PNG file.
Clear Field - clears the automaton field.

Editing Rules

The Edit Rules option allows you to define automaton rules:

Each rule has a symbol assigned. For example, the Conway's Game of Life automaton has a symbol: S23 / B3. The first number S indicates the number of alive neighbours necessary for a cell to survive to the next generation. The second number B indicates the number of alive neighbours necessary for a cell to be born in the next generation.

There is also an option to include the cell itself as its own "neighbour". This way the cell can have nine neighbours rather than eight:

Editing Colors

The Edit Colors option allows you to choose colors and the number of shades for the visual representation of the automaton.

For example:

With two colors, let's say purple and white, the cells can only be purple or white.
With multiple shades, the cells can have intermediate colors which, in case of purple and white, are shades of purple.

When a cell reaches its end color (in our example, purple), there are two possibilities:

The color jumps to the beginning - the white color.
The color changes back gradually from the end color (purple) toward the beginning (white).

The above two choices are provided by the Wrap color switch:

Changing the Initial Cell Density

The initial cell density determines the initial number of cells in the automaton field. The following two examples illustrate:

A field with low initial cell density:

A field with high initial cell density:

Drawing in the Automaton Field

You can also draw the initial state of the automaton field with a mouse or with fingers (on touch devices). While you can draw the field any time, even when a simulation is running, a good starting point is to clear the field first by choosing the Clear Field option:

After that, you can draw whatever you want and then start the simulation to see how your drawing ends up. You can keep drawing while the simulation is running.

The following pictures show the Majority Automaton field before and after running a simulation:

Sample Automata

The app comes with a set of 14 sample automata. Below, there are three examples of the sample cellular automata.

Majority Automaton

Symbol: S56789 / B56789

The Majority Automaton's rules include the central cell as its own neighbour. This way every cell has nine neighbours:

The Majority Automaton's rules say:

The cell dies when it has four or less neighbours.
The cell is born when it has five or more neighbours.

It means that only the cells with the majority of neighbours being alive are able to survive or be born.

Below, there is a picture of the Majority Automaton after several generations. It quickly creates a stable pattern that stops changing over time:

Moore's Automaton

Symbol: S46789 / B46789

The Moore's Automaton's rules differ slightly from the Majority Automaton's rules:

If a cell has four, six, or more neighbours the cell stays alive or is born.
If a cell has less than four or five neighbours the cell dies.

This small change creates a different pattern. Unlike the Majority Automaton, the Moore's Automaton is unstable -- the edges of the black areas are in constant turmoil.

This is the Moore's automaton simulation after 100 generations:

After 2,000 generations, the edges start to smooth out:

Because of its unstable nature, the Moore's Automaton is well-suited for visualization using shades. Here, we set 40 shades between white and green colors:

Game of Life

Symbol: S23 / B3

One of the most famous cellular automaton is the Game of Life created by the British mathematician John Conway with the following rules:

Any live cell with fewer than two live neighbours dies.
Any live cell with two of three live neighbours survives to the next generation.
Any live cell with more than three neighbours dies (from overpopulation).
Any dead cell with exactly three neighbours becomes alive (reproduction)

The rules generate a wide variety of shapes that even have their own names: beehive, loaf, boat, blinker, toad, and many more.

Other Automata

There are a few more sample automata in the app. A few of them achieve a stable state quite quickly. Others churn for a while before stabilizing. There is also an automaton that can go both ways depending on the initial layout of cells: it can go on forever, generating new patterns or it can stabilize. It’s the Black Waves automaton:

Below there are pictures of other sample automata:

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