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Drawing the pseudo-arc. (English) Zbl 1211.54047
Authors’ 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? 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 pseudo-arc 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 \(n\)-crooked 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.

MSC:
54F15 Continua and generalizations
54-04 Software, source code, etc. for problems pertaining to general topology
54H20 Topological dynamics (MSC2010)
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