Conways Game of Life simulation in Excel

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Tushar Mehta

4 thoughts on “Conways Game of Life simulation in Excel”

Using an array formula for the grid allows it to be done in one formula (as Excel calcs the entire grid in one go for each iteration). See http://www.oaltd.co.uk/Excel for my Life.zip file from 1996.

For those interested, here is the vba code to generate the 256 elementary CAs (pages 55-56 of “A New Kind of Science” by Stephen Wolfram…

each rule (0-255) begins with 7 different initial conditions (1-7)…

Sub Main()

c = 0
For x = 1 To 256
Range(Cells(3 + c, 2), Cells(8 + c, 7)).Select
With Selection
.HorizontalAlignment = xlCenter
.VerticalAlignment = xlCenter
.MergeCells = True
End With
Range(Cells(3 + c, 2), Cells(8 + c, 7)).Select
With Selection.Font
.Name = “Arial”
.Size = 24
End With
Range(Cells(3 + c, 2), Cells(8 + c, 7)) = x – 1
c = c + 18
Next

g9 = 0
For g7 = 0 To 1
For g6 = 0 To 1
For g5 = 0 To 1
For g4 = 0 To 1
For g3 = 0 To 1
For g2 = 0 To 1
For g1 = 0 To 1
For g0 = 0 To 1
g5c = 0
For cc = 1 To 7
Cells(1 + g9, 3 + g5c) = g7
Cells(1 + g9, 4 + g5c) = g6
Cells(1 + g9, 5 + g5c) = g5
Cells(1 + g9, 6 + g5c) = g4
Cells(1 + g9, 7 + g5c) = g3
Cells(1 + g9, 8 + g5c) = g2
Cells(1 + g9, 9 + g5c) = g1
Cells(1 + g9, 10 + g5c) = g0
If cc > 3 Then a1 = 1 Else a1 = 0
If cc = 2 Or cc = 3 Or cc = 6 Or cc = 7 Then b1 = 1 Else b1 = 0
If cc = 1 Or cc = 3 Or cc = 5 Or cc = 7 Then c1 = 1 Else c1 = 0
Cells(1 + g9, 10 + g5c + 2) = a1
Cells(1 + g9, 10 + g5c + 3) = b1
Cells(1 + g9, 10 + g5c + 4) = c1
g5c = g5c + 35
Next
g9 = g9 + 18
Next
Next
Next
Next
Next
Next
Next
Next

s = 0
For n = 1 To 256
sp = 18
sp2 = 0
For ics = 1 To 7
If ics = 1 Or ics = 3 Or ics = 5 Or ics = 7 Then Cells(1 + s, sp + 1 + sp2).Interior.ColorIndex = 48
If ics = 2 Or ics = 3 Or ics = 6 Or ics = 7 Then Cells(1 + s, sp + sp2).Interior.ColorIndex = 48
If ics > 3 Then Cells(1 + s, sp – 1 + sp2).Interior.ColorIndex = 48
a = -1
b = 1
c = 0
p1 = 1
For x = 2 + s To sp + s – 1
p1 = p1 + 1
ctr = “”
If Cells(1 + s, 10 + sp2) = 1 Then ctr = c
If Cells(1 + s, 10 + sp2) = 1 And Cells(1 + s, 3 + sp2) = 1 Then ctr = 1
For y = a To b
With Cells(x, sp + sp2 + y)
.Borders(xlEdgeLeft).LineStyle = 1
.Borders(xlEdgeTop).LineStyle = 1
.Borders(xlEdgeBottom).LineStyle = 1
.Borders(xlEdgeRight).LineStyle = 1
If ctr = 1 And y = a And p1 <> 2 Then
Cells(x – 1, sp + sp2 + y – 1).Interior.ColorIndex = 48
Cells(x – 1, sp + sp2 + y).Interior.ColorIndex = 48
End If
If Cells(x – 1, sp + sp2 + y – 1) = “” Then v1 = 0 Else v1 = 32
If Cells(x – 1, sp + sp2 + y) = “” Then v3 = 0 Else v3 = 16
If Cells(x – 1, sp + sp2 + y + 1) = “” Then v5 = 0 Else v5 = 8
If Cells(x – 1, sp + sp2 + y – 1).Interior.ColorIndex <> 48 Then v2 = 0 Else v2 = 4
If Cells(x – 1, sp + sp2 + y).Interior.ColorIndex <> 48 Then v4 = 0 Else v4 = 2
If ctr = 1 And y + 1 = b And p1 <> 2 Then
Cells(x – 1, sp + sp2 + y + 1).Interior.ColorIndex = 48
Cells(x – 1, sp + sp2 + y + 2).Interior.ColorIndex = 48
End If
If Cells(x – 1, sp + sp2 + y + 1).Interior.ColorIndex <> 48 Then v6 = 0 Else v6 = 1
T = v1 + v2 + v3 + v4 + v5 + v6
If T = 0 Or T = 8 Or T = 16 Or T = 24 Or T = 32 Or T = 40 Or T = 48 Or T = 56 Then
Cells(x, sp + sp2 + y) = 0
If Cells(1 + s, 10 + sp2) = 1 Then
Cells(x, sp + sp2 + y).Interior.ColorIndex = 48
End If
End If
If T = 1 Or T = 9 Or T = 17 Or T = 25 Or T = 33 Or T = 41 Or T = 49 Or T = 57 Then
If Cells(21, 19) = 9 Then MsgBox 9
Cells(x, sp + sp2 + y) = 1
If Cells(1 + s, 9 + sp2) = 1 Then
Cells(x, sp + sp2 + y).Interior.ColorIndex = 48
End If
End If
If T = 2 Or T = 10 Or T = 18 Or T = 26 Or T = 34 Or T = 42 Or T = 50 Or T = 58 Then
Cells(x, sp + sp2 + y) = 2
If Cells(1 + s, 8 + sp2) = 1 Then
Cells(x, sp + sp2 + y).Interior.ColorIndex = 48
End If
End If
If T = 3 Or T = 11 Or T = 19 Or T = 27 Or T = 35 Or T = 43 Or T = 51 Or T = 59 Then
Cells(x, sp + sp2 + y) = 3
If Cells(1 + s, 7 + sp2) = 1 Then
Cells(x, sp + sp2 + y).Interior.ColorIndex = 48
End If
End If
If T = 4 Or T = 12 Or T = 20 Or T = 28 Or T = 36 Or T = 44 Or T = 52 Or T = 60 Then
Cells(x, sp + sp2 + y) = 4
If Cells(1 + s, 6 + sp2) = 1 Then
Cells(x, sp + sp2 + y).Interior.ColorIndex = 48
End If
End If
If T = 5 Or T = 13 Or T = 21 Or T = 29 Or T = 37 Or T = 45 Or T = 53 Or T = 61 Then
Cells(x, sp + sp2 + y) = 5
If Cells(1 + s, 5 + sp2) = 1 Then
Cells(x, sp + sp2 + y).Interior.ColorIndex = 48
End If
End If
If T = 6 Or T = 14 Or T = 22 Or T = 30 Or T = 38 Or T = 46 Or T = 54 Or T = 62 Then
Cells(x, sp + sp2 + y) = 6
If Cells(1 + s, 4 + sp2) = 1 Then
Cells(x, sp + sp2 + y).Interior.ColorIndex = 48
End If
End If
If T = 7 Or T = 15 Or T = 23 Or T = 31 Or T = 39 Or T = 47 Or T = 55 Or T = 63 Then
Cells(x, sp + sp2 + y) = 7
If Cells(1 + s, 3 + sp2) = 1 Then
Cells(x, sp + sp2 + y).Interior.ColorIndex = 48
End If
End If
End With
Next
a = a – 1
b = b + 1
If ctr <> “” Then
If c = 0 Then c = 1 Else c = 0
End If
Next
sp2 = sp2 + 35
Next
s = s + 18
Next

MsgBox “the end”
Cells(6, 12).Select