def coords(i,j,m,n):
coords = []
ioffs=[-1, 0, 1, 1, 1, 0, -1, -1]
joffs=[-1, -1, -1, 0, 1, 1, 1, 0]
for joff, ioff in zip(joffs, ioffs):
if j + joff >= 0 and j + joff < m:
if i + ioff >= 0 and i + ioff < m:
coords.append((j+joff,i+ioff))
return coords
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def step(A):
m = A.nrows()
n = A.ncols()
B = copy(A)
for i in range(A.nrows()):
for j in range(A.ncols()):
cs = coords(i,j,m,n)
for k,l in cs:
if A[k,l] > 0:
B[k,l] -= 0.1*A[k,l]
B[i,j] += 0.1*A[k,l]
return B
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A = zero_matrix(RR, 4,4)
A[A.nrows()/2,A.ncols()/2] = 1
l = []
print sum(sum(A))
a = animate([matrix_plot(A)])
for i in range(100):
A = step(A)
a = a * animate([matrix_plot(A)])
a.show()
1.00000000000000 1.00000000000000 
|
"""Second attempt, trying to divert diffusion out of the edges"""
'Second attempt, trying to divert diffusion out of the edges' 'Second attempt, trying to divert diffusion out of the edges' |
def step2(A):
m = A.nrows()
n = A.ncols()
B = copy(A)
netFlow = 0.1
for i in range(A.nrows()):
for j in range(A.ncols()):
cs = coords(i,j,m,n)
perCellFlow = netFlow/len(cs)
for k,l in cs:
if A[k,l] > 0:
B[k,l] -= perCellFlow*A[k,l]
B[i,j] += perCellFlow*A[k,l]
return B
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A = zero_matrix(RR, 6,6)
A[A.nrows()/2,A.ncols()/2] = 1
print sum(sum(A))
a = animate([matrix_plot(A)])
for i in range(100):
A = step2(A)
a = a * animate([matrix_plot(A)])
a.show()
1.00000000000000 1.00000000000000 
|
"""third attempt"""
'third attempt' 'third attempt' |
def pytha(k,l):
if not 0 in (k,l):
return sqrt(2)
else:
return 1
def step3(A):
m = A.nrows()
n = A.ncols()
B = copy(A)
netFlow = 0.1
for i in range(A.nrows()):
for j in range(A.ncols()):
cs = coords(i,j,m,n)
perCellFlow = netFlow/len(cs)
for k,l in cs:
if A[k,l] > 0:
B[k,l] -= perCellFlow * pytha(k,l) * A[k,l]
B[i,j] += perCellFlow * pytha(k,l) * A[k,l]
return B
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A = zero_matrix(RR, 6,6)
A[A.nrows()/2,A.ncols()/2] = 1
print sum(sum(A))
a = animate([matrix_plot(A)])
for i in range(100):
A = step3(A)
a = a * animate([matrix_plot(A)])
a.show()
1.00000000000000 1.00000000000000 |
"Fourth"
'Fourth' 'Fourth' |
def coords4(i,j,m,n):
coords = []
ioffs=[ 0, 1, 0, -1]
joffs=[-1, 0, 1, 0]
for joff, ioff in zip(joffs, ioffs):
if j + joff >= 0 and j + joff < m:
if i + ioff >= 0 and i + ioff < m:
coords.append((j+joff,i+ioff))
return coords
def step4(A):
m = A.nrows()
n = A.ncols()
B = copy(A)
netFlow = 0.1
for i in range(A.nrows()):
for j in range(A.ncols()):
cs = coords4(i,j,m,n)
perCellFlow = netFlow/len(cs)
for k,l in cs:
B[k,l] -= perCellFlow * A[k,l]
B[i,j] += perCellFlow * A[k,l]
return B
A = zero_matrix(RR, 6,6)
A[A.nrows()/2,A.ncols()/2] = 1
l = []
print sum(sum(A))
a = animate([matrix_plot(A)])
for i in range(100):
A = step4(A)
a = a * animate([matrix_plot(A)])
a.show()
1.00000000000000 1.00000000000000 
|
"Fifth"
'Fifth' 'Fifth' |
def coords5(i,j,m,n):
coords = []
ioffs=[ 0, 1, 0, -1]
joffs=[-1, 0, 1, 0]
for joff, ioff in zip(joffs, ioffs):
if j + joff >= 0 and j + joff < m:
if i + ioff >= 0 and i + ioff < m:
coords.append((j+joff,i+ioff))
return coords
def step5(A):
m = A.nrows()
n = A.ncols()
B = copy(A)
netFlow = 0.9
for i in range(A.nrows()):
for j in range(A.ncols()):
cs = coords5(i,j,m,n)
perCellFlow = netFlow/len(cs)
B[j,i] -= netFlow * A[j,i]
for k,l in cs:
B[k,l] += perCellFlow * A[j,i]
return B
A = zero_matrix(RR, 6,6)
A[A.nrows()/2,A.ncols()/2] = 1
l = []
print sum(sum(A))
a = animate([matrix_plot(A)])
for i in range(10):
A = step5(A)
a = a * animate([matrix_plot(A)])
a.show()
1.00000000000000 1.00000000000000 
|
def coords6(j,i,m,n):
coords = []
ioffs=[ 0, 1, 0, -1]
joffs=[-1, 0, 1, 0]
for joff, ioff in zip(joffs, ioffs):
coords.append(((j + joff) % m, (i+ioff)%n))S
return coords
def step6(A):
m = A.nrows()
n = A.ncols()
B = copy(A)
netFlow = 0.1
for i in range(A.nrows()):
for j in range(A.ncols()):
cs = coords6(i,j,m,n)
perCellFlow = netFlow/len(cs)
B[j,i] -= netFlow * A[j,i]
for k,l in cs:
B[k,l] += perCellFlow * A[j,i]
return B
A = zero_matrix(RR, 6,6)
A[A.nrows()/2,A.ncols()/2] = 1
print sum(sum(A))
a = animate([matrix_plot(A)])
for i in range(10):
A = step5(A)
a = a * animate([matrix_plot(A)])
a.show()
Traceback (click to the left of this block for traceback) ... SyntaxError: invalid syntax Traceback (most recent call last): return coords
File "", line 1, in <module>
File "/tmp/tmpCP6NYe/___code___.py", line 8
coords.append(((j + joff) % m, (i+ioff)%n))S
^
SyntaxError: invalid syntax
|
def coords7(i,j,m,n):
coords = []
ioffs=[ 0, 1, 0, -1]
joffs=[-1, 0, 1, 0]
for joff, ioff in zip(joffs, ioffs):
coords.append(((j+joff)%m,(i+ioff)%n))
return coords
def step7(A):
m = A.nrows()
n = A.ncols()
B = copy(A)
netFlow = 0.1
for i in range(A.nrows()):
for j in range(A.ncols()):
cs = coords4(i,j,m,n)
perCellFlow = netFlow/len(cs)
for k,l in cs:
B[k,l] -= perCellFlow * A[k,l]
B[i,j] += perCellFlow * A[k,l]
return B
A = zero_matrix(RR, 6,6)
A[A.nrows()/2,A.ncols()/2] = 1
l = []
print sum(sum(A))
a = animate([matrix_plot(A)])
for i in range(100):
A = step7(A)
a = a * animate([matrix_plot(A)])
a.show()
1.00000000000000 1.00000000000000 
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