Julia Fractals in Postscript Fractal Geometry II
Kees van der Laan EUROTEX 2012 & 6CM PROCEEDINGS 47 Julia fractals in PostScript Fractal Geometry II In memory of Hans Lauwerier Abstract Lauwerier’s BASIC codes for visualization of the usual Julia fractals: JULIAMC, JULIABS, JULIAF, JULIAD, JULIAP, of the Mandelbrot fractal MANDELx, MANDIS, MANDET and his codes for the advanced circular symmetric Julia fractals JULIAS, JULIASYMm, JULIASYM, FRACSYMm, as well as the classical 1D bifurcation picture Collet, have been converted into PostScript defs. Examples of use are included. A glimpse into Chaos theory, in order to understand the principles and peculiarities underlying Julia sets, is given. Bifurcation diagrams of the Ver- hulst model of limited growth and of the Julia quadratic dynamical system — M-fractal — have been included. Barnsley’s triples: fractal, IFS and equivalent dynamical system are in- troduced. How to use the beginnings of colours in PostScript is explained. How to obtain Julia fractals via Stuif’s Julia fractal viewer, and via the special fractal packages Winfract, XaoS, and Fractalus is dealt with. From BASIC codes to PostScript library defs entails soft- ware engineering skills. The paper exhibits experimental fractal geometry, practical use of minimal TEX, as well as ample EPSF programming, and is the result of my next step in ac- quainting myself with Lauwerier’s 10+ years work on fractals. Keywords Acrobat Pro, Adobe, art, attractor, backtracking, Barnsley, BASIC, bifurcation, Cauchy con- vergence, chaos, circle symmetry, dynamical systems, EPSF, escape-time algorithm, Feigen- baum constant, fractal dimension D, Fractalus package, FIFO, fractal geometry, IDE (Inte- grated development Environment), IFS (Iterated Function System), Julia, Lauwerier, Man- delbrot, mathematical software, minimal encapsulated PostScript, minimal plain TeX, Monte Carlo, μ-geometry, periodic doubling, Photoshop, PSlib, PSView, repeller, self-similarity, software engineering, Stuif’s previewer, TEXworks, (adaptable) user space, Verhulst growth model, Winfract package, XaoS fractal package.
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