Lewis, Wayne, Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409 (firstname.lastname@example.org) and Minc, Piotr, Department of Mathematics and Statistics, Auburn University, Auburn, Alabama 36849 (email@example.com).
Drawing the pseudo-arc, pp. 905-934.
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.