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ResourceFunction["MultiwaySystem"][{"A""BBB","BB""A"},{"A"},6,"StatesGraph","IncludeStepNumber"True]
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ResourceFunction["MultiwaySystem"][{"A""BBB","BB""A"},{"A"},6,"BranchialGraph"]
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At every step, we take every state, and apply a function to it....
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MultiwayNestList[f_List,states_List,t_Integer]:=NestList[Flatten[Outer[Construct,f,#,1]]&,states,t]
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MultiwayNestList[{-1-#&,#&},{1},5]
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MultiwayNestList[{1+(1+I)#/2&,1+(1-I)#/2&},{1},4]
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ComplexListPlot[Flatten[MultiwayNestList[{1+(1+I)#/2&,1+(1-I)#/2&},{1},8]],PlotStylePointSize[.01]]
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ComplexListPlot[Flatten[Last@MultiwayNestList[{1+(1+I)#/2&,1+(1-I)#/2&},{1},12]],PlotStylePointSize[.01]]
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What happens with path weighting?
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Counts[Values[Counts[Last@MultiwayNestList[{1+(1+I)#/2&,1+(1-I)#/2&},{1},7]]]]
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1108,210
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Counts[Values[Counts[Last@MultiwayNestList[{1+(1+I)#/2&,1+(1-I)#/2&},{1},8]]]]
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1210,223
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Counts[Values[Counts[Last@MultiwayNestList[{1+(1+I)#/2&,1+(1-I)#/2&},{1},9]]]]
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1412,250
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ComplexListPlot[Flatten[Last@MultiwayNestList[{1+(-1+I)#/2&,1+(-1-I)#/2&},{1},12]],PlotStylePointSize[.01]]
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1D version
1D version
Analogy
Analogy
Ordinary multiway system has states with discrete labeling, e.g. ABBBAAAA
Ordinary multiway system has states with discrete labeling, e.g. ABBBAAAA
First step: use continuous numbers to represent states : i.e. there is a natural geometry on the set of states
First step: use continuous numbers to represent states : i.e. there is a natural geometry on the set of states
Analog of causal invariance is various questions about the growth rate of distinct numbers (and the dimension of the limit set)
What is the analog of branchial space? What is its relation to the geometry of states?
What is the analog of branchial space? What is its relation to the geometry of states?
I.e. the geometry of state space is probably the same as the geometry of branchial space
What is the analog of rulial space?
What is the analog of rulial space?
Start from z=1, then apply 1 ± α z for all values of α
If |α| < 1/2 all trees are Cantor-like
Above some modulus of α