Eric Weeks - personal pages - misc / pictures

# Contour plots with trigonometric functions

See the bottom of the page for links to other simple algorithms like this one.

weeks@physics.emory.edu

### I originally got this idea from a Scientific American column -- the Computer Recreations column sometime in the mid-80's, discussing moire patterns. However, I ended up discovering these interesting non-moire patterns.

NEW: Download a windows version of this program, written by Luciano Genero. Just click the program and it runs, automatically cycling through various parameters. Hit Esc to end. These are contour plots of a special trigonometric function. I calculate the function:

#### z = E sin(A sin(I x) + B cos(J y)) + F cos(C cos (K x) + D sin(L y))

This function has parameters A-F and I-L which I can choose to be whatever I want. If they are all equal to one, you get this picture: If they are all equal to two, you get this picture: Both of these pictures are periodic.

The original Scientific American article actually was not about these sorts of pictures. I discovered the nice pictures that formula makes by myself. The article discussed plotting pictures where Z changed so rapidly that you got moire effects, like Z=X^2 + Y^2. I found that I liked these pictures better than I liked the moire pictures. I made a small animation that wanders somewhat through the different parameters. Click the picture to see the animation.

Also, I started a simple shell script running which varied all of the values randomly, and came up with a wide variety of pictures. Some of them are below. Any values not listed are equal to one (for most of these pictures, I=J=K=L=1 for example).  A=1.86 B=4.43 C=4.77 D=5.34 E=0.77 F=0.28 I=2.17 J=2.05 K=1.17 L=2.13 A=2.86 B=1.78 C=4.61 D=2.80 E=0.48 F=0.51 I=0.91 J=3.00 K=1.75 L=0.67 A=1.70 B=3.87 C=4.78 D=5.29 E=0.59 F=0.49 A=5.98 B=3.09 C=2.35 D=4.79 E+0.47 F=0.49 I=0.88 J=2.70 K=1.29 L=0.43 A=3.90 B=7.10 C=9.30 D=2.90 E=0.84 F=0.84 If you'd like to see more, click on the pictures below:        Click here to see EIGHTEEN more of these pictures. For some reason some people do not seem to be overloaded with yellow and red pictures by this point; if this is you, I put 18 of the best of the rest on that page. ### Software

gcc -o tplot trigplot3.c -lm • Odds and Ends: These are various tiny ideas that are simple to do which make interesting pictures, or are otherwise interesting (to me). Click one of the pictures below to see others.      Simple trigonometric plot | Double-trigonometric contour plot | Lissajous figures | Simple diffusion limited aggregation | Spiral triangles | Polar flowers