Created
September 19, 2018 11:50
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#2D-Turing pattern陰解法 | |
#参考:三浦岳、発生の数理、京都大学学術出版会、2015、6.6 | |
#julia v0.6 | |
#using FFTW | |
using Plots | |
gr(size=(320,300),titlefont=font("sans-serif",9)) | |
dx=0.04 | |
N=convert(Int,1/dx) #gridSize=25 | |
dt=0.02 | |
dp=0.0002 | |
dq=0.01 | |
f(u,v)=u+dt*(0.6*u-v-u.^3) | |
g(u,v)=v+dt*(1.5*u-2*v) | |
kernelU=zeros(N,N) | |
kernelU[1,1]=1+4*dt*dp/dx/dx | |
kernelU[2,1] =-dt*dp/dx/dx | |
kernelU[end,1]=-dt*dp/dx/dx | |
kernelU[1,end]=-dt*dp/dx/dx | |
kernelU[1,2] =-dt*dp/dx/dx | |
kernelV=zeros(N,N) | |
kernelV[1,1]=1+4*dt*dq/dx/dx | |
kernelV[2,1] =-dt*dq/dx/dx | |
kernelV[end,1]=-dt*dq/dx/dx | |
kernelV[1,end]=-dt*dq/dx/dx | |
kernelV[1,2] =-dt*dq/dx/dx | |
ku=1./(fft(kernelU)) | |
kv=1./(fft(kernelV)) | |
function oneStep(u,v) | |
u=ifft(ku.*fft(f(u,v))) | |
v=ifft(kv.*fft(g(u,v))) | |
return u,v | |
end | |
uI=rand(N,N)*0.01 | |
vI=rand(N,N)*0.01 | |
u=uI | |
v=vI | |
#= | |
for i in 1:100 | |
u,v=oneStep(u,v) | |
end | |
u | |
=# | |
anim = @animate for m in 0:3000 | |
t=round(m*dt,3) | |
heatmap(real(u), | |
title="t = $t", | |
aspect_ratio=:equal | |
) | |
u,v=oneStep(u,v) | |
end every 25 | |
@time gif(anim,"tmp/6_6_2D_pattern_inkaihou_320.gif",fps=4) |
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