Iconizer: Examples |
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Michael Field and Martin Golubitsky give the parameter settings for most of the images in their book Symmetry In Chaos. Twelve of these have been conveniently built into Iconizer and are accessed via the Examples 1 and Examples 2 items on the main menu. Field and Golubitsky often call the resulting images Icons. However, as 'icon' has become an over-used word, Symmetric Icons is to be preferred.
By using Iconizer the examples from Symmetry In Chaos can be coloured differently. The parameters can be drifted away from the book's values to see how this alters the resulting image. Iconizer brings the book to life.
It could have been the case that Symmetry In Chaos had exhausted the images that could be generated from the dihedral logistic mapping. An internet search in February 2010 revealed only a few images that are not in the book. These seemed to be variations on existing themes. Possibly this is because Symmetry In Chaos was first published in 1992 and the computers of that time made exploring the dihedral logistic mapping slow and awkward. Even so, it is surprising that the topic has not been revisited more recently. Whatever: Iconizer in 2010 has revealed that this equation has more to it than one might have thought from a quick Google search.
Iconizer contains twelve examples all of which are very different to anything in Field and Golubitsky's book. One of these was presented earlier in this Users' Guide as a sample image. For the time being, the remainder are a motivation to buy the Iconizer software. :-)
The dihedral logistic mapping has yet to reveal all of its secrets. Iconizer is the tool needed to take the exploration onward.
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