TuringPattern1D.jl

#1D-Turing pattern
#参考：三浦岳、発生の数理、京都大学学術出版会、2015、6.3
#julia v0.6
using Plots
gr()

dx=0.02
dt=0.01
N=convert(Int,1/dx)

dp=0.0002
dq=0.01

pInitial=rand(N)*0.01 #50-element Array
qInitial=rand(N)*0.01

f(p,q)=0.6*p-q-p.^3
g(p,q)=1.5*p-2*q

diffusion(v)=circshift(v,1)+circshift(v,-1)-2*v
diffusionP(v)=dp*diffusion(v)/(dx*dx)
diffusionQ(v)=dq*diffusion(v)/(dx*dx)

function pqAfterDt(p,q)
    p=p+dt*(f(p,q)+diffusionP(p))
    q=q+dt*(g(p,q)+diffusionQ(q))
    return p,q
end

#pqAfterDt(pInitial,qInitial)

p=pInitial
q=qInitial

anim = @animate for m=0:6000
    plot([p,q],
        #xticks=0:1:20,
        ylim=(-0.7,0.7),
        yticks=-0.0:0.1:0.7,
        #seriestype=:bar,
        title="gen = $m",
        label=["Activator","Inhibitor"])
    p,q=pqAfterDt(p,q)
end every 30
@time gif(anim,"tmp/6_3_Turing_pattern.gif",fps=4)