Python, 101101 86
x=[0]*63x=' '*31
x[31]=1x+='.'+x
exec"print''exec"print x;x=''.join(map' .'[x[i-1]!=x[i-62]]for i in range(str,x63));x=[a^b for;"*32
This is longer, but prettier.
x=' a,b'*31
x+=u'Δ'+x
exec inu"print zipx;x=''.join(x[1:]+x[:1],x[-1:]+x[:u' Δ'[x[i-1]!=x[i-62]]for i in range(63)];"*32);"*32
Edit: playing with strings directly, got rid of obnoxiously long slicing, made output prettier.
000000000000000000000000000000010000000000000000000000000000000 Δ
000000000000000000000000000000101000000000000000000000000000000 Δ Δ
000000000000000000000000000001000100000000000000000000000000000 Δ Δ
000000000000000000000000000010101010000000000000000000000000000 Δ Δ Δ Δ
000000000000000000000000000100000001000000000000000000000000000 Δ Δ
000000000000000000000000001010000010100000000000000000000000000 Δ Δ Δ Δ
000000000000000000000000010001000100010000000000000000000000000 Δ Δ Δ Δ
000000000000000000000000101010101010101000000000000000000000000 Δ Δ Δ Δ Δ Δ Δ Δ
000000000000000000000001000000000000000100000000000000000000000 Δ Δ
000000000000000000000010100000000000001010000000000000000000000 Δ Δ Δ Δ
000000000000000000000100010000000000010001000000000000000000000 Δ Δ Δ Δ
000000000000000000001010101000000000101010100000000000000000000 Δ Δ Δ Δ Δ Δ Δ Δ
000000000000000000010000000100000001000000010000000000000000000 Δ Δ Δ Δ
000000000000000000101000001010000010100000101000000000000000000 Δ Δ Δ Δ Δ Δ Δ Δ
000000000000000001000100010001000100010001000100000000000000000 Δ Δ Δ Δ Δ Δ Δ Δ
000000000000000010101010101010101010101010101010000000000000000 Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ
000000000000000100000000000000000000000000000001000000000000000 Δ Δ
000000000000001010000000000000000000000000000010100000000000000 Δ Δ Δ Δ
000000000000010001000000000000000000000000000100010000000000000 Δ Δ Δ Δ
000000000000101010100000000000000000000000001010101000000000000 Δ Δ Δ Δ Δ Δ Δ Δ
000000000001000000010000000000000000000000010000000100000000000 Δ Δ Δ Δ
000000000010100000101000000000000000000000101000001010000000000 Δ Δ Δ Δ Δ Δ Δ Δ
000000000100010001000100000000000000000001000100010001000000000 Δ Δ Δ Δ Δ Δ Δ Δ
000000001010101010101010000000000000000010101010101010100000000 Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ
000000010000000000000001000000000000000100000000000000010000000 Δ Δ Δ Δ
000000101000000000000010100000000000001010000000000000101000000 Δ Δ Δ Δ Δ Δ Δ Δ
000001000100000000000100010000000000010001000000000001000100000 Δ Δ Δ Δ Δ Δ Δ Δ
000010101010000000001010101000000000101010100000000010101010000 Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ
000100000001000000010000000100000001000000010000000100000001000 Δ Δ Δ Δ Δ Δ Δ Δ
001010000010100000101000001010000010100000101000001010000010100 Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ
010001000100010001000100010001000100010001000100010001000100010 Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ
101010101010101010101010101010101010101010101010101010101010101Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ