Drawing the pseudo-arc

Wayne Lewis, Piotr Minc

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

It is very likely that the pseudo-arc may occur as an attractor of some natural dynamical system. How would a picture of such a strange attractor look like? Would it be recognized as the pseudo-arc, a hereditarily indecomposable continuum? This paper shows that it could be difficult. We notice that no black and white image can look hereditarily indecomposable on any raster device (like a computer screen or a printed page). We also try to generate the best computer picture of the pseudo-arc as it is possible under the circumstances. With that purpose in mind, we expand the pseudoarc into an inverse limit with relatively simple, deterministically defined and easy to handle numerically n-crooked bonding maps. We use this expansion to assess numerical complexity of drawing the pseudo-arc with help from the Anderson-Choquet embedding theorem. We also generate graphs of ncrooked maps with large n's, and we prove that a rasterized image of such a graph does not look very crooked at all because it must contain a long straight linear vertical segment.

Original languageEnglish
Pages (from-to)905-934
Number of pages30
JournalHouston Journal of Mathematics
Volume36
Issue number3
StatePublished - 2010

Keywords

  • Computer generated image
  • Crooked map
  • Hereditarily indecomposable continuum
  • Pseudo-arc
  • Pseudoarc
  • Raster graphics
  • Strange attractors

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