In - Depth Coverage of the Icon Programming Language
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چکیده
It has long been known that modular arithmetic often produces interesting numerical patterns. These patterns can be made easier to comprehend and more interesting by rendering them as images with colors associated with numerical values. The example most often cited is Pascal's Triangle , which exhibits the binomial coefficients. If you take the coefficients modulo m for various m, you get different but interesting patterns. Figures 1 through 3 show a portion of Pascal's Triangle for m = 2, 3, and 5, using m uniformly spaced shades of gray from black (for 0) to white (for m–1). See References 1 and 2 for extensive treatments of this subject. Our interest in the subject came from a paper entitled " Carpets and Rugs: An Exercise in Numbers " [3]. This brief and informal paper describes the results of generating integers on a square array according to a " neighborhood " rule. The results are reduced modulo m and colored according to the resulting values. Computing the values of the elements of an array according to the values of their neighbors is the basis for cellular automata [4,5]. Cellular au-tomata may be one dimensional, two dimensional, or of higher dimension. The two-dimensional Game of Life is the best known [6].
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10. Avoid long lines. Instead, continue expressions on as many lines as are needed for easy readability. See the first two issues of The Icon Analyst for the proper techniques for breaking lines. Similarly, continue long string and cset literals on several lines if that’s necessary to make them readable. See Appendix A of the second edition of The Icon Programming Language for the method of con...
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