Some work on 4&5
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@ -35,6 +35,9 @@ First we define an $N \times N$ random matrix. The $i$th element is 1 with proba
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In percolation theory, we have a *critical probability*, $p_c$ which is for $p < p_c$ we have no percolation and for $p > p_c$ our system percolates. Our aim is to find the value of $p_c$, but for now we must code the lattice and percolation.
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"""
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# ╔═╡ 8aa6eaee-9238-4e74-bffc-606f08562ea4
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pl₁ = simshow(repeat((sample(1:-1:0, weights([0.75, 1-0.75]), (100,100))), inner = (10, 10)))
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# ╔═╡ ea1f7206-eea0-4014-a4fb-3c5f5e78660e
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md""" p= $(@bind p NumberField(0.01:0.01:1, default = 0.5))"""
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@ -73,20 +76,30 @@ md" Nₜ = $(@bind Nₜ NumberField(50:200))"
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# ╔═╡ 47d8f7ec-0d76-4309-9beb-3c288489cb1a
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md""" Number of Trials = $(@bind n_trials NumberField(1:200))"""
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# ╔═╡ 5d74efcc-4699-4a45-95d5-1029581f84aa
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plot(pₛ,(Q./50), label = "Percolation probability")
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# ╔═╡ 5e2613e5-5f81-4d24-8e21-708039344754
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# ╠═╡ disabled = true
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#=╠═╡
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begin
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# ╔═╡ 340be4d1-e325-4e8d-b791-e6af5bd2e610
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plot(Q[findall(diff(Q) .!= 0)]./50 .+ findlast(Q .== 0))
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p_cs = []
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# ╔═╡ 1823f63d-e0f0-4867-a762-3ab234717e5f
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Qₛᵢ = findall(x -> x != 0 && x != 50, Q)
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# ╔═╡ d812351e-5bcc-4de0-a0b0-3bb56f328391
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Qₛᵢ[21]
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# ╔═╡ 158d3a9c-c435-437e-bf0c-e184ef0e68d1
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Qₛ = sum(Q)/length(Q)
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for trial in 1:n_trials
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lat = sample(1:-1:0, weights([p₁, 1-p₁]), (Nₜ,Nₜ))
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pₛ = length(findall(lat .== 0)):-1:1
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for i in pₛ
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zero_idxs = findall(lat .== 0)
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iᵣ = zero_idxs[rand(1:length(zero_idxs))]
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lat[iᵣ] = 1
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Pₜ = percolation2D(lat)
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if isPercolated2D(Pₜ)
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Cₚ = count(lat .== 0)/(Nₜ^2)
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push!(p_cs,Cₚ)
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break
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end
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end
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end
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end
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╠═╡ =#
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# ╔═╡ ffb6129f-303d-4cb4-a8c1-fb5b1e9c1fb9
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md"""## Usefull Functions"""
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@ -172,21 +185,15 @@ function visualizeV2D(P)
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free = RGB(1.0, 1.0, 1.0)
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blue = RGB(0.1, 0.2, 0.9)
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comm = intersect(P[1, :], P[end, :]) # Common values in top and buttom of P
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# Remove 0s and 1s
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deleteat!(comm, comm .== 0)
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deleteat!(comm, comm .== 1)
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m,n = size(P)
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pic = zeros(RGB, m, n)
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pic[P .> 1] .= blue
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pic[P .== 0] .= block
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pic[P .> 1] .= free
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if isPercolated2D(P)
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pic[P .== comm[1]] .= blue
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end
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pic
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pic[P .== 1] .= free
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simshow(repeat((pic), inner = (10, 10)))
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end
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# ╔═╡ 69a26f6f-476d-469b-8ab4-bd1c39cf139d
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@ -258,14 +265,6 @@ isPercolated2D(P)
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# ╔═╡ 53f6ad3e-2bed-450a-ac8b-afba6ed328ef
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visualize2D(P)
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# ╔═╡ 3c7cb57d-91b3-4f0a-a0f7-3f202b48fe57
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p_cs
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# ╔═╡ 86be6a6c-ec68-49c6-a3ce-aa7cce5398c3
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if length(p_cs)>0
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sum(p_cs)/length(p_cs)
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end
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# ╔═╡ 3972be44-ac1d-482f-9fe1-69c51c0815c4
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begin
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pₛ = p₁:ϵ:p₂
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@ -288,30 +287,16 @@ begin
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end
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end
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# ╔═╡ 5e2613e5-5f81-4d24-8e21-708039344754
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# ╠═╡ disabled = true
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#=╠═╡
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begin
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# ╔═╡ 5d74efcc-4699-4a45-95d5-1029581f84aa
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plot(pₛ,(Q./n_trials), label = "Percolation probability")
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p_cs = []
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# ╔═╡ 3c7cb57d-91b3-4f0a-a0f7-3f202b48fe57
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p_cs
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for trial in 1:n_trials
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lat = sample(1:-1:0, weights([p₁, 1-p₁]), (Nₜ,Nₜ))
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pₛ = length(findall(lat .== 0)):-1:1
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for i in pₛ
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zero_idxs = findall(lat .== 0)
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iᵣ = zero_idxs[rand(1:length(zero_idxs))]
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lat[iᵣ] = 1
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Pₜ = percolation2D(lat)
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if isPercolated2D(Pₜ)
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Cₚ = count(lat .== 0)/(Nₜ^2)
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push!(p_cs,Cₚ)
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break
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end
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end
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end
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# ╔═╡ 86be6a6c-ec68-49c6-a3ce-aa7cce5398c3
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if length(p_cs)>0
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sum(p_cs)/length(p_cs)
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end
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╠═╡ =#
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# ╔═╡ 00000000-0000-0000-0000-000000000001
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PLUTO_PROJECT_TOML_CONTENTS = """
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@ -1858,6 +1843,7 @@ version = "1.4.1+0"
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# ╔═╡ Cell order:
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# ╟─d541a835-801c-46d7-b311-9f712ffb0eb0
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# ╠═efa19006-6cc2-4180-8963-2b5b20affdcf
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# ╠═8aa6eaee-9238-4e74-bffc-606f08562ea4
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# ╟─ea1f7206-eea0-4014-a4fb-3c5f5e78660e
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# ╟─7fff47f2-0795-4f4f-aa51-7dc0adf6992c
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# ╠═18c0fbf2-07b1-4ec3-b364-2ce24ebf5a2a
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@ -1872,10 +1858,6 @@ version = "1.4.1+0"
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# ╟─47d8f7ec-0d76-4309-9beb-3c288489cb1a
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# ╠═3972be44-ac1d-482f-9fe1-69c51c0815c4
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# ╠═5d74efcc-4699-4a45-95d5-1029581f84aa
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# ╠═340be4d1-e325-4e8d-b791-e6af5bd2e610
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# ╠═1823f63d-e0f0-4867-a762-3ab234717e5f
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# ╠═d812351e-5bcc-4de0-a0b0-3bb56f328391
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# ╠═158d3a9c-c435-437e-bf0c-e184ef0e68d1
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# ╠═5e2613e5-5f81-4d24-8e21-708039344754
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# ╠═3c7cb57d-91b3-4f0a-a0f7-3f202b48fe57
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# ╠═86be6a6c-ec68-49c6-a3ce-aa7cce5398c3
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@ -1885,7 +1867,7 @@ version = "1.4.1+0"
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# ╟─1251afa5-fc38-4967-9596-11c21f1b0322
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# ╟─a4e70668-fb6d-4a5f-8326-feda865193d5
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# ╠═c728553c-4d9d-4111-b3a1-6cffd64a472b
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# ╟─ac0c427d-b9d1-48bc-8b8e-25fb1734c8f0
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# ╠═ac0c427d-b9d1-48bc-8b8e-25fb1734c8f0
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# ╟─69a26f6f-476d-469b-8ab4-bd1c39cf139d
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# ╟─00000000-0000-0000-0000-000000000001
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# ╟─00000000-0000-0000-0000-000000000002
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