Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wireworld Package  | |
The functions defined in the Wireworld` package provide tools for exploring the Wireworld Turing-complete cellular automaton.
Load the package:
In[316]:=
<<Wireworld`
States and Cells
States and Cells
Wireworld is a cellular automaton which can be in one of four different cells:
0 | an empty cell |
1 | an electron head |
2 | an electron tail |
3 | a wire cell |
Wireworld cells.
Electron heads are considered alive. Electron cells and wire cells are considered to be dead.
Wireworld is a two-dimensional cellular automaton, which means a valid state must be a matrix where each element is one of the cells mentioned above:
test whether expr |
Testing valid Wireworld states.
Here is a valid Wireworld state:
In[44]:=
 | WireworldStateQ |
Out[44]=
True
Sparse arrays can also be matrices:
In[51]:=
| WireworldStateQ |
 |  |
|
Out[51]=
True
State Visualization and Edition
State Visualization and Edition
plot a Wireworld state |
Plotting a Wireworld state.
Plot a Wireworld state:
In[318]:=
| WireworldPlot |
|  |
|
Out[318]=
draw a Wireworld state with dimensions {d,h} | |
edit a Wireworld state |
Drawing Wireworld states.
Open a window to draw a Wireworld state with 12 rows and 22 columns:
| WireworldDraw |
Edit an already existing Wireworld state:
| WireworldDraw |
| |
|
To obtain the drawn state, press the key:
"Return"
In[317]:=
| WireworldDraw |
Out[317]=
SparseArray
|  |
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Wire Rules
Wire Rules
As mentioned before, Wireworld is a two-dimensional . It uses the Moore neighborhood, which means the evolution of any one cell depends on all neighbours that are one cell away in any direction.
In each generation:
1
.Wire cells with 1 or 2 live neighbours (electron heads) turn into electron heads
2
.Electron heads turn into electron tails
3
.Electron tails turn into wire cells
Empty cells are just that: empty cells. They neither change nor interact with the other cells.
evolve a Wireworld state init t |
Evolving a Wireworld state.
Compute the evolution of a Wireworld state for 3 steps:
In[359]:=
| WireworldEvolve |
|  |
|
Out[359]=
SparseArray
,SparseArray
,SparseArray
,SparseArray
| |
|
|  |
|
|  |
|
|  |
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Electrons
Electrons
An electron consists of a head and a tail. Along a line of wire cells, it will propagate in the direction pointed by the head.
An electron moving along a wire:
In[366]:=
GraphicsColumn
/@
SparseArray
,3
 | WireworldPlot |
 | WireworldEvolve |
|  |
|
Out[366]=
Electrons can turn around corners:
An electron meets a fork in the road:
An electron caught in a loop will go around it forever:
Split off a fork from the loop to create an electron source:
The Diode
The Diode
A diode allows the flow of electrons in only one direction:
An electron flowing the "right" way through a diode:
An electron flowing the "wrong" way through a diode:
Logic Gates
Logic Gates
An OR gate fed by two electron sources:
An XOR gate fed by two electron sources: