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Contour plots with trigonometric functionsSee the bottom of the page for links to other simple algorithms like this one.
|Selected as a "Knot a Braid of Links" site, #248 (Oct 27, 2001).|
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:
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 the source code. To compile:
This page created August 22, 1996.