Building the APL atlas of natural shapes

ABSTRACT

It was previously shown [1] that APL contained the most powerful idiom ≠\ that could be used, directly in the language all computers know: binary algebra, to build models as well for physics as for biology and computer science. Several papers on the subject were published or submitted inside the "APL world" as well as outside (Bibliography in [2]). The purpose of the present paper is to show how a classical model, built to generate fractal shapes in plane geometry (2-D) can be revisited and considerably extended, thanks to the properties of ≠\ and of array-oriented binary algebra.

REFERENCES

• 1: G.A. Langlet, Unitary Theory of Information, APL-CAM Journal, Belgium, Vol 13, No 2, p. 399,432 (Part I) & No 3, p. 709-743 (Part II) (1991).
• 2: Gérard A. Langlet, Towards the ultimate APL-TOE, ACM SIGAPL APL Quote Quad, v.23 n.1, p.118-134, July 1992
• 3: G.A. Langlet, L'Int~gration Binaire, C16 de l'Irr~versibilit~ du Temps, 13th Int. Congress on Cybernetics, Namur, Belgium, (Aug. 1992).
• 4: G.A. Langlet, Physique et Alg~bre de Boole, Les Nouvelles d'APL, AFAPL, Paris, No 3, (April 1992).
• 5: G.A. Langlet, Un Concours Paritonesque, APL-CAM Journal, Belgium, Vol. 14, No 3, p. 412-416 (July 1992).
• 6: G.A. Langlet, La Propagation Asym6trique de la Parit~ Biomath, ISSN 0035.10.24, vol. 115, p. 5-42 (1992).
• 7: G.A. Langlet, L'lnt~gration Binaire par l'Image, APL-CAM Journal, Vol. 14, No 3. p. 389-406 (July 1992).
• 8: Howard A. Peelle, Encoding gray codes in APL, ACM SIGAPL APL Quote Quad, v.7 n.3, Fall 1976 [doi>10.1145/585987.585993]
• 9: ISO8495e/f, Int. APL Standard, ISO, CH-Gen~ve (1989).
• 10: G.A. Langlet, Le Principe de Moindre Action G~n6ralisie, UITF 1992 Rennes, ISI3N 2-9009947-00-9 p. 77,96 (Dec. 1992).
• 11: G.A. Langlet, Variations sur Sierpinski Pascal & Fibonacci, APL-CAM Journal, Vol 13, No 2, p. 375-389 (1991).
• 12: G.A. Langlet, The Fractal Laws of Genetics, Biomath, ISSN 0035.10.24, vol. 118, p. 60-71 (1992).
• 13: G.A. Langlet, DNA-style Programming for Genetic Simulations ,APL-CAM Journal, Vol. 14, No 3, p. 407-411 (July 1992).
• 14: R.F. Voss, in The Science of Fractal Images (Peitgen & Saupe, eds), Springer, NY, ISBN 0.387,96608,0 (1988).
• 15: R.V. Jean, Cha the Origins of Spiral Symmetry in Plants, in: /.Argittai & C.A. Pickover (eds), Spiral Symmetry, World Scientific, Singapore, ISBN 981-02-0615-1 (1992) p. 323-351.
• 16: R.V. Jean, Mathematical Approach to Pattern and Form in Plant Growth, J. Wiley & Sons, New York, USA, ISBN 0-471-88357-3 (1984); Growth Matrix, p. 144.
• 17: James A. Brown , Sandra Pakin , Raymond P. Polivka, APL2: at a glance, Prentice-Hall, Inc., Upper Saddle River, NJ, 1988
• 18: G.A. Langlet, New Mathematics for the Computer, Tool of Thought, ACM/SIGAPL, (New York, NY, jan. 23, 1993).
• 19: S. Wolfram, Theory and Apphcations of Cellular Automata, World Scientific, ISBN 9971-50-123-6, p. 11, 52, 131 (1986).

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.4 Graphics Utilities
          Subjects: Graphics packages

Additional Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: APL
      D.3.3 Language Constructs and Features
          Subjects: Procedures, functions, and subroutines

  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.2 Nonnumerical Algorithms and Problems
          Subjects: Geometrical problems and computations

General Terms:
Algorithms, Languages, Theory