last pattern wip

src/fhn_solver.jl

@@ -57,7 +57,7 @@ function step_fhn!(U, V, params_obs::Observable; dx=1)
 
     # Define one integration step using your fhn! function
     prob = ODEProblem((du, u, p, t) -> fhn!(du, u, p, t), u_init, (0.0, 0.1), p)
-    sol = solve(prob, Tsit5(); dt=0.1, save_start=false, saveat=10.0)
+    sol = solve(prob, BS3(); save_start=false, saveat=10.0)
 
     # Extract solution and reshape
     u_new = reshape(sol[end][1:p.N^2], p.N, p.N)
@@ -67,6 +67,17 @@ function step_fhn!(U, V, params_obs::Observable; dx=1)
     U .= u_new
     V .= v_new
 
+    # Apply periodic boundary conditions
+    U[1, :] .= U[end-1, :]
+    U[end, :] .= U[2, :]
+    U[:, 1] .= U[:, end-1]
+    U[:, end] .= U[:, 2]
+
+    V[1, :] .= V[end-1, :]
+    V[end, :] .= V[2, :]
+    V[:, 1] .= V[:, end-1]
+    V[:, end] .= V[:, 2]
+
     return U
 end
 

src/utils/laplacian.jl

@@ -11,6 +11,6 @@ function laplacian(U::AbstractMatrix{<:Real}, dx::Real)
     return (up .+ down .+ left .+ right .- 4 .* center) ./ h2
 end
 
-export laplacian, laplacian5
+export laplacian
 
 end # module Laplacian

src/utils/templates.jl

@@ -1,7 +1,8 @@
+# helper functions for filling cells in specific places of the matrix
+# Not all functions are used. Those are for experimenting and debugging purposes
 
 module Templates
 
-# helper functions for filling cells in specific places of the matrix
 function blocks_ic(N)
     u = fill(1.0, N, N)
     v = fill(0.0, N, N)
@@ -9,9 +10,9 @@ function blocks_ic(N)
 
     function safe_block!(u, row_center, col_center)
         row_start = max(row_center - 8, 1)
-        row_end   = min(row_center + 7, N)
+        row_end = min(row_center + 7, N)
         col_start = max(col_center - 8, 1)
-        col_end   = min(col_center + 7, N)
+        col_end = min(col_center + 7, N)
         u[row_start:row_end, col_start:col_end] .= -0.01
     end
 
@@ -35,6 +36,17 @@ function column_ic(N)
     return u, v
 end
 
+function stripe_ic(N)
+    u = zeros(N, N)
+    v = zeros(N, N)
+    for i in 1:N
+        for j in 1:N
+            u[i, j] = 0.1 + 0.05 * sin(2π * j / 10) + 0.01 * randn()
+        end
+    end
+    return u, v
+end
+
 function two_rows_edge_distance_ic(N)
     row_width = 8
     distance_from_edge = 50
@@ -126,7 +138,7 @@ function three_circles_random_ic(N)
         end
     end
 
-    return vec(u), vec(v)
+    return u, v
 end
 
 function squiggle_ic(N, Lx=400.0, Ly=400.0)
@@ -151,7 +163,7 @@ function squiggle_ic(N, Lx=400.0, Ly=400.0)
     v = fill(vplus, N, N)
 
     # Apply squiggle
-    u[Z .> 0.8] .= uminus
+    u[Z.>0.8] .= uminus
 
     return vec(u), vec(v)
 end
@@ -160,7 +172,7 @@ function coral_ic(N)
     u = fill(0.534522, N, N)
     v = fill(0.381802, N, N)
 
-    for _ in 1:40  # place 15 noisy seeds
+    for _ in 1:20  # place 15 noisy seeds
         i, j = rand(10:N-10), rand(10:N-10)
         u[i-2:i+2, j-2:j+2] .= -0.534522 .+ 0.2 * rand(5, 5)
     end
@@ -168,6 +180,6 @@ function coral_ic(N)
     return u, v
 end
 
-export blocks_ic, column_ic, squiggle_ic, three_circles_random_ic, circle_ic, center_band_ic, two_rows_edge_distance_ic
+export blocks_ic, column_ic, squiggle_ic, three_circles_random_ic, circle_ic, center_band_ic, two_rows_edge_distance_ic, coral_ic
 
 end

src/visualization.jl

@@ -43,6 +43,7 @@ function reset!(U, V, heat_obs)
     radius = 10
     U[center-radius:center+radius, center-radius:center+radius] .= 0.50
     V[center-radius:center+radius, center-radius:center+radius] .= 0.25
+
     heat_obs[] = copy(U)
 end
 
@@ -101,8 +102,9 @@ function build_ui(U, V, param_obs_map::NamedTuple, params_obs, heat_obs)
     gh[1, 2] = templategrid = GridLayout(ax.scene, tellwidth=false)
     templategrid[1, 1] = Label(fig, "Templates:")
     btn_zebra = Button(templategrid[1, 2], width=100, label="Zebra Stripes")
-    btn_cheetah = Button(templategrid[1, 3], width=100, label="Cheetah Spots")
+    btn_cow = Button(templategrid[1, 3], width=100, label="Cow Spots")
-    btn_coral = Button(templategrid[1, 4], width=100, label="Coral Pattern")
+    btn_cheetah = Button(templategrid[1, 4], width=100, label="Cheetah Spots")
+    #btn_coral = Button(templategrid[1, 4], width=100, label="Coral Pattern")
 
     # place all the parameter boxes
     gh[2, 2] = textboxgrid = GridLayout(ax.scene, tellwidth=false)
@@ -130,7 +132,7 @@ function build_ui(U, V, param_obs_map::NamedTuple, params_obs, heat_obs)
         colsize!(textboxgrid, c, Relative(0.1))
     end
 
-    # Events ##############################################################
+    # ======== Events ========
     # Timer and state for animation
     running = Observable(false)
 
@@ -163,6 +165,7 @@ function build_ui(U, V, param_obs_map::NamedTuple, params_obs, heat_obs)
 
     on(btn_reset.clicks) do _
         running[] = false
+        hm.colormap[] = :viridis
         reset!(U, V, heat_obs)
 
     end
@@ -172,24 +175,40 @@ function build_ui(U, V, param_obs_map::NamedTuple, params_obs, heat_obs)
         # add column to center of matrix
         U, V = Templates.column_ic(params_obs[].N)
 
-        hm.colormap[] = :berlin
+        hm.colormap[] = :grayC
 
         # change params
-        param_obs_map.Du[] = 0.016
+        param_obs_map.Du[] = 1.0
-        param_obs_map.Dv[] = 0.1
+        param_obs_map.Dv[] = 2.0
-        param_obs_map.ϵ[] = 0.1
+        param_obs_map.ϵ[] = 0.3
-        param_obs_map.a[] = 0.5
+        param_obs_map.a[] = 0.0
-        param_obs_map.b[] = 0.9
+        param_obs_map.b[] = 1.4
         heat_obs[] = copy(U)
     end
 
     # Template Control
+    on(btn_cow.clicks) do _
+        # fill matrix with random noise
+        U = 0.05 .* (2 .* rand(params_obs[].N, params_obs[].N) .- 1)  # noise in [-0.05, 0.05]
+        V = 0.05 .* (2 .* rand(params_obs[].N, params_obs[].N) .- 1)
+
+        hm.colormap[] = :grayC
+
+        # change params
+        param_obs_map.Du[] = 1.0
+        param_obs_map.Dv[] = 10.0
+        param_obs_map.ϵ[] = 0.01
+        param_obs_map.a[] = -0.1
+        param_obs_map.b[] = 1.2
+        heat_obs[] = copy(U)
+    end
+
     on(btn_cheetah.clicks) do _
         # fill matrix with random noise
         U = 0.05 .* (2 .* rand(params_obs[].N, params_obs[].N) .- 1)  # noise in [-0.05, 0.05]
         V = 0.05 .* (2 .* rand(params_obs[].N, params_obs[].N) .- 1)
 
-        hm.colormap[] = :magma
+        hm.colormap[] = cgrad(:lajolla, rev = true)
 
         # change params
         param_obs_map.Du[] = 0.182
@@ -200,21 +219,6 @@ function build_ui(U, V, param_obs_map::NamedTuple, params_obs, heat_obs)
         heat_obs[] = copy(U)
     end
 
-    # Template Control
-    on(btn_coral.clicks) do _
-        U, V = Templates.coral_ic(params_obs[].N)
-
-        hm.colormap[] = :plasma
-
-        # change params
-        param_obs_map.Du[] = 0.001
-        param_obs_map.Dv[] = 0.06
-        param_obs_map.ϵ[] = 0.05
-        param_obs_map.a[] = 0.0
-        param_obs_map.b[] = 1.2
-        heat_obs[] = copy(U)
-    end
-
     on(spoint) do pt
         r = 5
         if pt === nothing