Morphing Wallpaper Functions
Morphing Wallpaper Functions
This Demonstration morphs two wallpaper functions (z) and (z) using interpolation, such that on 25% of the domain on the left, on 25% on the right, and in the middle is a linear interpolation of the two functions [1, pp. 201–202].
f
1
f
2
g(z)=(z)
f
1
g(z)=(z)
f
2
We use functions such as (z)=1/2,+1/4a,, where =.
f
i
E
m
1
n
1
E
m
2
n
2
E
m,n
2πi(mX+nY)
e
Since producing these graphics might be slow, start with a low resolution using RGB colors, fix the lattice parameters and , then use a photograph.
f(z)