Papers on Fractal Geometry and Complex Bases

William J. Gilbert

1. W.J. Gilbert and R. James Green, Negative Based Number Systems, Math. Mag. 52 (1979), 240-244.
          [Math Reviews 82e:10001; Zentralblatt Math:418.10008]
2. W.J. Gilbert, Radix Representations of Quadratic Fields, J. Math. Analysis and Applications 83 (1981), 264-274.
          [Math Reviews 83m:12005; Zentralblatt Math:472.10011]
          [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.]
3. 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; Zentralblatt Math:508.12002]
4. W.J. Gilbert, Fractal Geometry derived from Complex Bases, Math. Intelligencer 4 (1982), 78-86.
          [Math Reviews 83m:10092; Zentralblatt Math:493.10010]
5. W.J. Gilbert, Complex Numbers with three radix expansions, Can. J. Math. 34 (1982), 1335-1348.
          [Math Reviews 85c:11013; Zentralblatt Math:494.10005]
6. W.J. Gilbert, Arithmetic in Complex Bases, Math. Magazine 57 (1984), 77-81.
          [Zentralblatt Math:539.10011]
7. W.J. Gilbert, A cube-filling Hilbert curve, Math. Intelligencer 6(3) (1984), p.78.
8. W.J. Gilbert, The Fractal Dimension of Sets derived from Complex Bases, Can. Math. Bull. 29 (1986), 495-500.
          [Math Reviews 88b:28014; Zentralblatt Math:564.10007]
9. W.J. Gilbert, Complex Bases and Fractal Similarity, Ann. Sc. Math. Quebec 11 (1987), 65-77.
          [Math Reviews 89a:11017; Zentralblatt Math:633.10008]
10. W.J. Gilbert, The Division Algorithm in Complex Bases, Can. Math. Bull. 39 (1996), 47-54.
           [Math Reviews 97a:11019; Zentralblatt Math:851.11004]
11. 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; Zentralblatt Math:870.68105]
12. W.J. Gilbert, Complex Based Number Systems (Manuscript)
           [formerly called Gaussian Integers as Bases for Exotic Number Systems (1989)]
13. 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.

Fractal Software

1. 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.]
2. 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.]