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Some Products and Sums of Sines and Cosines It is easy to visualize interference patterns using false coloring for height. Some of these playful examples appeared as "Product of three harmonics" [Abstract] in Cliff Pickover's The Pattern Book. Here we use magenta for the highest points and red for the lowest points. The wave patterns we explore are based upon:

c1=cos(x), c2=cos(y), c3=cos(r) 
s1=sin(x), s2=sin(y), s3=sin(r)
where r^2=x^2+y^2

c1 * c2	c1 * c3	c1 * c2 * c3
s1 * s2	s1 * s3	s1 * s2 * s3
c1 + c2	c1 + c3	c1 + c2 + c3
s1 + s2	s1 + s3	s1 + s2 + s3

Animation changing
from c1 + c2
to c1 + c2 + c3
to c1 + c3 (1.4M)

Animation changing
from s1 + s2
to s1 + s2 + s3
to s1 + s3 (1.3M)

Scripts and links
· A J script for creating some of these images: v3harm.ijs
· The script requires another J script for creating bitmaps files: raster5.ijs
· Cliff's Home Page
· Cliff's Gallery of Chaos, Fractals and Symmetry