Papers on Fractal Geometry and Complex Bases
William J. Gilbert
- W.J. Gilbert and R. James Green,
Negative Based Number Systems, Math. Mag. 52 (1979), 240-244.
[Math Reviews 82e:10001;
- W.J. Gilbert, Radix Representations of Quadratic Fields, J. Math. Analysis and Applications 83 (1981), 264-274.
[Math Reviews 83m:12005;
[also see Cubic CNS polynomials, notes on a conjecture of W.J. Gilbert by Shigeki Akiyama, Horst Brunotte and Attila Petho, J. Math. Anal. Appl. 281 (2003), 402-415.]
- W.J. Gilbert, Geometry of radix representations, in the Geometric Vein: The Coxeter Festschrift, edited by C. Davis et al., Springer, New York, 1981, 129-139.
[Math Reviews 83j:12001;
- W.J. Gilbert, Fractal Geometry derived from Complex Bases, Math. Intelligencer 4 (1982), 78-86.
[Math Reviews 83m:10092;
- W.J. Gilbert, Complex Numbers with three radix expansions, Can. J. Math. 34 (1982), 1335-1348.
[Math Reviews 85c:11013;
- W.J. Gilbert,
Arithmetic in Complex Bases, Math. Magazine 57 (1984), 77-81.
- W.J. Gilbert, A cube-filling Hilbert curve, Math. Intelligencer 6(3) (1984), p.78.
- W.J. Gilbert, The Fractal Dimension of Sets derived from Complex Bases, Can. Math. Bull. 29 (1986), 495-500.
[Math Reviews 88b:28014;
- W.J. Gilbert,
Complex Bases and Fractal Similarity, Ann. Sc. Math. Quebec 11 (1987), 65-77.
[Math Reviews 89a:11017;
- W.J. Gilbert, The Division Algorithm in Complex Bases, Can. Math. Bull. 39 (1996), 47-54.
[Math Reviews 97a:11019;
- J.-P. Allouche, E. Cateland, W.J. Gilbert, H.-O. Peitgen, J.O. Shallit,
and G. Skordev, Automatic Maps in Exotic Numeration Systems,
Theory of Computing Systems
30 (1997), 285-331.
[Math Reviews 98a:68114;
- W.J. Gilbert, Complex Based Number Systems (Manuscript)
[formerly called Gaussian Integers as Bases for Exotic Number Systems (1989)]
- J.C. Beatty, Raster Graphics and Color, The Amer. Statistician, 37 (1983), 60-75
contains a coloured photograph of the complex base 1-i, by W.J. Gilbert on page 68.
- W.J. Gilbert: Julia Program written in Objective C for the NeXT computer only and distributed on CD ROMs called monoLib (monolithic Library) produced by monoChrome Systems, Edison, N.J. (1992) [The program with source was on the PEAK and PEANUTS NeXT Archives, but these are gone now.]
- W.J. Gilbert: Rational Mandelbrot Set Program (RatMandel) written in Objective C for the NeXT computer only and distributed on the Big Green CD ROM 4.0, Skylee Press, San Francisco (1994) [The program with source was on the PEAK and PEANUTS NeXT Archives, but these are gone now.]
The home page of William Gilbert
This page was last updated on
29 November 2013
by W. Gilbert