list manipulation – Trouble Iterating My Simulated Forest Fire

I’m having some trouble iterating my simulation of a forest fire. I’m new to mathematica, so apologies for poor coding. I’m sure there are far neater and more efficient ways of doing this, but i would like to know whats the problem with the method im using currently if possible.

This is my code to get the adjacent elements, including ‘wrap around’:

neighbourPos(m_, i_, j_) := Transpose(Mod({i, j} + {{-1, 0, 1, 0}, {0, -1, 0, 1}}, Dimensions(m),));

For the fire, 2s represent burning trees, 1s trees and 0s empty ground. After one timestep, trees adjacent to a fire will set on fire and original fire(s) will burn themselves out and become ‘0s’. This my code to simulate the spread of the fire:

nextState(m_) :=  
 (firepos = Position(m, 2); 
  a = MapAt(2 # &, m, 
    neighbourPos(m, Position(m, 2)((1, 1)), Position(m, 2)((1, 2)))); 
  MapAt(0 &, a, firepos))

It seems to work. Up to a point anyway. I would like to eventually plot the thing with ListAnimate, however, When i try to iterate nextState until the fire is burnt out with FixedPointList it stops working properly after 6 iterations and i get a load of errors.

e.g

MatrixPlot(mat/2, PlotRange -> {0, 1}, ColorFunction -> "Rainbow", ColorFunctionScaling -> False)

Gives

Starting matrix

Then

MatrixPlot(nextState(mat)/2, PlotRange -> {0, 1}, ColorFunction -> "Rainbow",  ColorFunctionScaling -> False)

Matrix after one iteration

But then errors come after more iterations.

In(1):= fireStates(m_) := FixedPointList(nextState, m);

In(14):= frames = fireStates(mat);

During evaluation of In(14):= Part::partw: Part 1 of {} does not exist.

During evaluation of In(14):= Part::partw: Part 1 of {} does not exist.

During evaluation of In(14):= MapAt::pkspec1: The expression Mod(1+{}((1,1)),10,1) cannot be used as a part specification.

During evaluation of In(14):= Thread::tdlen: Objects of unequal length in Mod({{0,1,2,1},{1,0,1,2}},{3},1) cannot be combined.

During evaluation of In(14):= MapAt::psl: Position specification Transpose(Mod({{0,1,2,1},{1,0,1,2}},{3},1)) in MapAt(2 #1&,MapAt(2 #1&,<<1>>,{{Mod(-1+{}((1,1)),10,1),Mod({}((1,2)),10,1)},{<<1>>,Mod(<<1>>)},<<1>>,{Mod({}((1,1)),10,1),Mod(1+{}((1,2)),10,1)}}),Transpose(Mod({{0,1,2,1},{1,0,1,2}},{3},1))) is not a machine-sized integer or a list of machine-sized integers.

During evaluation of In(14):= MapAt::partw: Part {3,4,2,1,2,3} of MapAt(2 #1&,MapAt(2 #1&,<<1>>,{{Mod(-1+{}((1,1)),10,1),Mod({}((1,2)),10,1)},{<<1>>,Mod(<<1>>)},<<1>>,{Mod({}((1,1)),10,1),Mod(1+{}((1,2)),10,1)}}),Transpose(Mod({{0,1,2,1},{1,0,1,2}},{3},1))) does not exist.

During evaluation of In(14):= Thread::tdlen: Objects of unequal length in Mod({{1,2,3,2},{1,0,1,2}},{3},1) cannot be combined.

During evaluation of In(14):= MapAt::psl: Position specification Transpose(Mod({{1,2,3,2},{1,0,1,2}},{3},1)) in MapAt(2 #1&,MapAt(0&,MapAt(2 #1&,MapAt(<<1>>),Transpose(Mod(<<1>>))),{{1,1,1},{3,1,2,1,3},{3,2,2,1,2,3},{3,3,2,1,3},{3,4,2,1,2,3}}),Transpose(Mod({{1,2,3,2},{1,0,1,2}},{3},1))) is not a machine-sized integer or a list of machine-sized integers.

During evaluation of In(14):= MapAt::partw: Part {2,2,3,4,2,1,2,3} of MapAt(2 #1&,MapAt(0&,MapAt(2 #1&,MapAt(<<1>>),Transpose(Mod(<<1>>))),{{1,1,1},{3,1,2,1,3},{3,2,2,1,2,3},{3,3,2,1,3},{3,4,2,1,2,3}}),Transpose(Mod({{1,2,3,2},{1,0,1,2}},{3},1))) does not exist.

During evaluation of In(14):= Thread::tdlen: Objects of unequal length in Mod({{1,2,3,2},{1,0,1,2}},{3},1) cannot be combined.

During evaluation of In(14):= General::stop: Further output of Thread::tdlen will be suppressed during this calculation.

During evaluation of In(14):= MapAt::psl: Position specification Transpose(Mod({{1,2,3,2},{1,0,1,2}},{3},1)) in MapAt(2 #1&,MapAt(0&,MapAt(<<1>>),{{2,1,1,1},{2,2,1,1,1},{2,2,3,1,2,1,3},{2,2,3,2,2,1,2,3},<<3>>,{2,3,1,1,2,4},{3,2,3},{3,3,2},<<5>>}),Transpose(Mod({{1,2,3,2},{1,0,1,2}},{3},1))) is not a machine-sized integer or a list of machine-sized integers.

During evaluation of In(14):= General::stop: Further output of MapAt::psl will be suppressed during this calculation.

During evaluation of In(14):= MapAt::partw: Part {2,2,2,2,3,4,2,1,2,3} of MapAt(2 #1&,MapAt(0&,MapAt(<<1>>),{{2,1,1,1},{2,2,1,1,1},{2,2,3,1,2,1,3},{2,2,3,2,2,1,2,3},<<3>>,{2,3,1,1,2,4},{3,2,3},{3,3,2},<<5>>}),Transpose(Mod({{1,2,3,2},{1,0,1,2}},{3},1))) does not exist.

During evaluation of In(14):= General::stop: Further output of MapAt::partw will be suppressed during this calculation.

Many many thanks in advance for anyone kind enough to help.

Cheers.

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matrix – Function representing a forest fire after one time step

How can I create a function that would have as its argument an array mat of 0s, 1s, and 2s where the 2s are burning trees and the function would give an array that represents the forest after one time step?

I have tried using

mat=RandomChoice[{0,1,2},{10,10}]
nextstep[mat_]:=Sequence[mat2 + {1, 0}, mat2 + {0, 1}, mat2 + {-1, 0}, mat2 + {0,-1}]

but that doesn’t seem to work. After one time step, every tree, represented by 1s, that is in the von Neumann neighborhood of a burning tree would catch fire, but the 0s, which means there are no trees, would remain the same.

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LIVE ~ 188.120.230.121:30033 | 0.237 | Moscow | 48 | Unknown | Russian Federation | Checked at vn5socks.net
LIVE ~ 101.6.64.148:7891 | 0.059 | Beijing | 22 | Unknown | China | Checked at vn5socks.net
LIVE ~ 188.120.229.151:30037 | 0.21 | Moscow | 48 | Unknown | Russian Federation | Checked at vn5socks.net
LIVE ~ 82.165.137.115:7061 | 0.182 | Unknown | Unknown | Unknown | Germany | Checked at vn5socks.net
LIVE ~ 188.120.230.75:30020 | 0.208 | Moscow | 48 | Unknown | Russian Federation | Checked at vn5socks.net
LIVE ~ 158.69.243.148:9999 | 0.264 | Lake Forest | CA | 92630 | United States | Checked at vn5socks.net


FireHeaven
Reviewed by FireHeaven on
.
[Vn5socks.net] Auto update 24/7 – Good socks 1h10 PM
LIVE ~ 139.59.244.84:38888 | 0.035 | Unknown | Unknown | Unknown | Australia | Checked at vn5socks.net
LIVE ~ 154.209.93.155:1281 | 0.074 | Unknown | Unknown | Unknown | Unknown | Checked at vn5socks.net
LIVE ~ 45.252.248.152:59745 | 0.025 | Unknown | Unknown | Unknown | Unknown | Checked at vn5socks.net
LIVE ~ 207.180.252.162:21000 | 0.186 | Buffalo | NY | 14221 | United States | Checked at vn5socks.net
LIVE ~ 88.255.106.27:1082 | 0.269 | Istanbul | 34 |

Rating: 5



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[Vn5socks.net] Auto update 24/7 – Good socks 11h10 PM


LIVE ~ 39.105.192.77:9999 | 0.068 | Unknown | Unknown | Unknown | Hong Kong | Checked at vn5socks.net
LIVE ~ 101.6.64.148:7891 | 0.058 | Beijing | 22 | Unknown | China | Checked at vn5socks.net
LIVE ~ 154.209.93.155:1281 | 0.074 | Unknown | Unknown | Unknown | Unknown | Checked at vn5socks.net
LIVE ~ 137.74.35.119:443 | 0.189 | Lachine | QC | Unknown | Canada | Checked at vn5socks.net
LIVE ~ 207.180.252.162:21000 | 0.181 | Buffalo | NY | 14221 | United States | Checked at vn5socks.net
LIVE ~ 113.128.37.156:64163 | 0.076 | Beijing | 22 | Unknown | China | Checked at vn5socks.net
LIVE ~ 188.166.34.137:9000 | 0.205 | Saint Petersburg | 66 | Unknown | Russian Federation | Checked at vn5socks.net
LIVE ~ 188.120.230.75:30020 | 0.208 | Moscow | 48 | Unknown | Russian Federation | Checked at vn5socks.net
LIVE ~ 158.69.243.148:9999 | 0.266 | Lake Forest | CA | 92630 | United States | Checked at vn5socks.net
LIVE ~ 51.89.27.240:14159 | 0.193 | Unknown | Unknown | Unknown | United Kingdom | Checked at vn5socks.net
LIVE ~ 192.99.57.210:1981 | 0.27 | Unknown | Unknown | Unknown | Unknown | Checked at vn5socks.net
LIVE ~ 218.64.122.99:7302 | 0.284 | Beijing | 22 | Unknown | China | Checked at vn5socks.net
LIVE ~ 188.120.229.151:30037 | 0.189 | Moscow | 48 | Unknown | Russian Federation | Checked at vn5socks.net
LIVE ~ 45.252.248.152:59745 | 0.032 | Unknown | Unknown | Unknown | Unknown | Checked at vn5socks.net
LIVE ~ 188.120.230.121:30033 | 0.187 | Moscow | 48 | Unknown | Russian Federation | Checked at vn5socks.net
LIVE ~ 24.249.199.14:57335 | 0.33 | Unknown | Unknown | Unknown | United States | Checked at vn5socks.net
LIVE ~ 82.165.137.115:7061 | 0.19 | Unknown | Unknown | Unknown | Germany | Checked at vn5socks.net
LIVE ~ 188.120.230.121:30020 | 0.211 | Moscow | 48 | Unknown | Russian Federation | Checked at vn5socks.net


FireHeaven
Reviewed by FireHeaven on
.
[Vn5socks.net] Auto update 24/7 – Good socks 11h10 PM
LIVE ~ 39.105.192.77:9999 | 0.068 | Unknown | Unknown | Unknown | Hong Kong | Checked at vn5socks.net
LIVE ~ 101.6.64.148:7891 | 0.058 | Beijing | 22 | Unknown | China | Checked at vn5socks.net
LIVE ~ 154.209.93.155:1281 | 0.074 | Unknown | Unknown | Unknown | Unknown | Checked at vn5socks.net
LIVE ~ 137.74.35.119:443 | 0.189 | Lachine | QC | Unknown | Canada | Checked at vn5socks.net
LIVE ~ 207.180.252.162:21000 | 0.181 | Buffalo | NY | 14221 | United States |

Rating: 5



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