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Neural nets as a continuum coordinatization of rulial space
Neural nets as a continuum coordinatization of rulial space
What is curvature?
What is curvature?
Neural net operator commutation
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NetInitialize[LinearLayer[]]
Analog of energy-momentum
Analog of energy-momentum
Perhaps training data
Microfluidics as an alternative continuum limit
Microfluidics as an alternative continuum limit
Continuous cellular automata as continuum limit
Continuous cellular automata as continuum limit
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NestList[Function[s,FractionalPart[3/2Total[RotateLeft[s,#]&/@{-1,0,1}]]],CenterArray[{1},10],10]
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Function[s,RotateLeft[s,#]&/@{-1,0,1}]@0,0,0,,,,0,0,0,0
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0,0,0,0,,,,0,0,0,0,0,0,,,,0,0,0,0,0,0,,,,0,0,0,0,0
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Total[%]
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0,0,,1,,1,,0,0,0
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ArrayPlot[NestList[Function[s,FractionalPart[3/2Total[RotateLeft[s,#]&/@{-1,0,1}]]],CenterArray[{1},100],50]]
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ArrayPlot[NestList[Function[s,FractionalPart[.6Total[RotateLeft[s,#]&/@{-1,0,1}]]],CenterArray[{1},100],50]]
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ArrayPlot[NestList[Function[s,FractionalPart[1.5/3Total[RotateLeft[s,#]&/@{-1,0,1}]]],CenterArray[{1},200],200]]
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Graph[#->CellularAutomaton[30][#]&/@Tuples[{1,0},3]]
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Graph[#->CellularAutomaton[30][#]&/@Tuples[{1,0},6]]
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Multiway Systems Based on Numbers
Multiway Systems Based on Numbers
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NestList[Union[Flatten[{#+1,2#}]]&,{0},5]
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{{0},{0,1},{0,1,2},{0,1,2,3,4},{0,1,2,3,4,5,6,8},{0,1,2,3,4,5,6,7,8,9,10,12,16}}
NestList[Union[Flatten[{a1#+b1,a2#b2}]]&,{0},5]
Related to Bernat’s trees ; tree convergence is related to causal invariance
Fully continuous multiway systems
Fully continuous multiway systems
PDE is continuous states and time, but 11 functions
Another case is continuous states [and time], but 1k functions