initial commit with project structure

Project.toml

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+[deps]
+DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa"
+GLMakie = "e9467ef8-e4e7-5192-8a1a-b1aee30e663a"

model_fhn.jl

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+function fhn!(du, u, p::FHNParams, t)
+    N, dx = p.N, p.dx
+
+    u_mat = reshape(u[1:N^2], N, N)
+    v_mat = reshape(u[N^2+1:end], N, N)
+
+    Δu = laplacian(u_mat) / dx^2
+    Δv = laplacian(v_mat) / dx^2
+
+    fu = p.Du * Δu .+ u_mat .- u_mat .^ 3 ./ 3 .- v_mat
+    fv = p.Dv * Δv .+ p.ε * (u_mat .+ p.a .- p.b .* v_mat)
+
+    du .= vcat(vec(fu), vec(fv))
+end

scripts/run_simulation.jl

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+include("../src/AnimalFurFHN.jl")  # this loads the module code
+using .AnimalFurFHN
+# include optional visualizer only if needed:
+include("../src/visualization.jl")
+using .Visualization
+
+N = 100
+tspan = (0.0, 100.0)
+
+sol = run_simulation(N, tspan)
+
+
+Visualization.step_through_solution(sol, N)

scripts/show_frame.jl

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+using GLMakie
+include("../src/AnimalFurFHN.jl")
+using .AnimalFurFHN
+
+# === Parameters ===
+N = 100
+tspan = (0.0, 100.0)
+frame_index = 1  # final time step
+
+# === Run simulation ===
+sol = run_simulation(N, tspan)
+
+# === Extract activator u ===
+u = sol.u[frame_index][1:N^2]
+u_mat = reshape(u, N, N)
+
+# === Plot ===
+fig = Figure()
+ax = Axis(fig[1, 1])
+heatmap!(ax, u_mat, colormap=:viridis)
+fig

src/AnimalFurFHN.jl

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+# src/AnimalFurFHN.jl
+module AnimalFurFHN
+
+include("constants.jl")
+include("initial_conditions.jl")
+include("laplacian.jl")
+include("model_fhn.jl")
+include("solver.jl")
+
+export run_simulation   # Make sure this is here!
+end

src/constants.jl

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+struct FHNParams
+    N::Int
+    dx::Float64
+    Du::Float64
+    Dv::Float64
+    ε::Float64
+    a::Float64
+    b::Float64
+end

src/initial_conditions.jl

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+function initial_conditions(N)
+    Random.seed!(1234)
+    u = 0.1 .+ 0.01 .* rand(N, N)
+    v = 0.1 .+ 0.01 .* rand(N, N)
+    return vec(u), vec(v)
+end

src/laplacian.jl

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+function laplacian(u, N, h)
+    U = reshape(u, N, N)
+    padded = circshift(U, (-1, 0)) .+ circshift(U, (1, 0)) .+
+             circshift(U, (0, -1)) .+ circshift(U, (0, 1)) .- 4 .* U
+    return vec(padded) ./ h^2
+end

src/model_fhn.jl

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+function fhn!(du, u, p::FHNParams, t)
+    N, dx = p.N, p.dx
+
+    u_mat = reshape(u[1:N^2], N, N)
+    v_mat = reshape(u[N^2+1:end], N, N)
+
+    Δu = laplacian(u_mat) / dx^2
+    Δv = laplacian(v_mat) / dx^2
+
+    fu = p.Du * Δu .+ u_mat .- u_mat .^ 3 ./ 3 .- v_mat
+    fv = p.Dv * Δv .+ p.ε * (u_mat .+ p.a .- p.b .* v_mat)
+
+    du .= vcat(vec(fu), vec(fv))
+end

src/solver.jl

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+function run_simulation(N::Int, tspan::Tuple{Float64,Float64})
+    # ✅ Turing pattern parameters — promotes stable spots
+    a = 0.1
+    b = 0.5
+    ϵ = 0.01
+    Du = 1e-5   # activator diffusion
+    Dv = 1e-3   # inhibitor diffusion (>> Du)
+
+    # Laplacian setup (assumes ∆x = 1)
+    dx = 1.0
+    L = laplacian_matrix(N, dx)
+
+    # ✅ Local random noise around a constant for initial conditions
+    u0, v0 = initial_conditions(N)  # Should include a seeded RNG
+    y0 = vcat(u0, v0)
+
+    # ODE system for Reaction-Diffusion with FitzHugh-Nagumo dynamics
+    function f!(du, u, p, t)
+        U = u[1:N^2]
+        V = u[N^2+1:end]
+
+        ΔU = Du .* (L * U)
+        ΔV = Dv .* (L * V)
+
+        du[1:N^2] = ΔU .+ (U .- (U .^ 3) ./ 3 .- V) ./ ϵ
+        du[N^2+1:end] = ΔV .+ ϵ .* (U .+ a .- b .* V)
+    end
+
+    # ✅ Use stiff solver for stability
+    prob = ODEProblem(f!, y0, tspan)
+    sol = solve(prob, Rosenbrock23(), saveat=1.0, reltol=1e-6, abstol=1e-6)
+
+    return sol
+end

src/visualization.jl

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+module Visualization
+
+using GLMakie
+
+function step_through_solution(sol, N)
+    fig = Figure(resolution=(600, 600))
+    ax = Axis(fig[1, 1])
+    slider = Slider(fig[2, 1], range=1:length(sol), startvalue=1)
+
+    # Initialize heatmap with first time step
+    u0 = reshape(sol[1][1:N^2], N, N)
+    heat_obs = Observable(u0)
+    hmap = heatmap!(ax, heat_obs, colormap=:magma)
+
+    # Update heatmap on slider movement
+    on(slider.value) do i
+        u = reshape(sol[i][1:N^2], N, N)
+        heat_obs[] = u
+    end
+
+    display(fig)
+end
+
+end