Poincaré Disk
This model is a two-dimensional visualization of the hyperbolic plane. It is the space
where Conway's Game of Life is played.
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Tiling
{
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Tiling Control
Change the entries in the input boxes to set the tiling {p,q} for the Poincaré Disk.
In this context:
p = the number of sides of the polygons
q = the number of polygons that meet at a vertex
Note that changing the values of p and q affects the number of neighbors that cell has. The number of neighbors can be found in the Simulation Data.
In this context:
p = the number of sides of the polygons
q = the number of polygons that meet at a vertex
Note that changing the values of p and q affects the number of neighbors that cell has. The number of neighbors can be found in the Simulation Data.
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Rule
Generic rule
Rule Selection
Updating
Rule Control
Choose the Rule Selection and Updating policies that the simulator will follow.
Rule Selection dictates which rule is chosen per generation. For the Rule Selection Policy, we have two options:
Rule Selection dictates which rule is chosen per generation. For the Rule Selection Policy, we have two options:
- Static = Only one rule is used for the entire run
- Dynamic = The rule selected for each generation cycles between three rules
- Synchronous = All cells update simultaneously every generation
- Asynchronous = Each cell updates independently with a probability of 0.5 (50%)
- Birthability = A dead cell is born in the next generation if it has x live neighbors
- Survivability = A live cell survives in the next generation if it has y live neighbors
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Saving and Loading Patterns
Save your own patterns and access them, as well as pattern presets, in a local
database. Additionally, export the current state of the simulator as an SVG file.
Save Button
Give your pattern a file name and click Save.
Open Button
The database will first display your saved patterns under the current tiling and rulestring of the simulator.
Save your current pattern configuration as an SVG file by right clicking on the image and choosing Save image as...
Save Button
Give your pattern a file name and click Save.
Open Button
The database will first display your saved patterns under the current tiling and rulestring of the simulator.
- To show other saved patterns under the same tiling with a different rulestring, select All Rules.
- To show other saved patterns under different tilings, select All Tilings. This will also enable access to the preset catalogue.
- To show pattern presets, make sure to select All Tilings then, select Presets.
Save your current pattern configuration as an SVG file by right clicking on the image and choosing Save image as...
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Export
Upload animation
Size:
Steps:
Frames/step:
Start:
End:
States
Speed
1 x
Simulator Control
This set of buttons can be used to control the simulator itself. The following are the
component functionalities in order:
- Reset the simulator
- Play the simulation continuously or Pause the simulation
- Move through the simulation by step
- Change the speed of the simulation
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Disk Control
The following are the button functionalities in order:
- Edit the state of the cells
- Move the Poincaré disk
- Recenter the disk at the origin
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Neighbors:
Population:
Generation:
Simulation Data
This section displays the number of neighbors of each
cell (based on the tiling), the current number of live cells in the
population, and how many
generations or timesteps have elapsed.
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Clusters
Cluster Navigation
This portion displays the cell clusters present on the Poincaré disk. Each cluster is
represented by two properties:
- Cluster No. = an ID to differentiate it from other clusters
- No. of Cells = the number of live cells present in the cluster
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