Photography, Mathematics and Art

Pure mathematicians are completely conversant with the creative nature of their research.  In fact, we refer to the Art of Mathematics. From out of nothing, almost, come ideas that, when fully developed, lead to wondrous new mathematical discoveries that time and time again subsequently find application in the real world.

Mathematics and Art are also closely connected.  For example, think of perspective.  Geometers and artists developed the ideas, and the latter put them to use in their paintings (see the work of the Venetian artist Canaletto for example).

I trained as a mathematician, but have also had a life long interest in painting, visiting galleries in many parts of the world.  Particularly appealing to me are the painters who, like Canaletto or the Flemish/Dutch painters of the 17th Century (Vermeer for example) use perspective.

Into more modern times, Albrecht Escher made wonderful use of the new discoveries in geometry (elliptical and hyperbolic geometries being prime examples – triangles always have more than 180 degrees in the former, which means that parallel lines always meet, or triangles always have less than 180 degree is the latter, in which case parallel lines diverge).

There are many Escher drawings with which you may be familiar.  Here’s one:

THE AMAZING WORLD OF M. C. ESCHER

Night and Day – M.C. Escher

One of my favourites, because it has its genesis in hyperbolic geometry, is:

Circle Limit III - M.C. Escer

Imagine my joy when I stumbled on a web site which enables one to create similar designs, but using one’s own images.  Here’s an example.  I started with the image below (how I made it is explained in the previous post):

DSC_0006 2012072306CircularMerge- ©Derek ChambersI then passed it through the Hyperbolic Tiling routine to get:

Hyperbolic Tiling Small- ©Derek ChambersWith a little further trickery, I then produced this:

Hyperbolic Tiling 1-1081 on BlackLighten- ©Derek Chambers- ©Derek ChambersI think that’s pretty neat.

And there are many more mathematical transformations which can be output as images on the website.

What’s its name.  Here you go: www.malinc.se and the hyperbolic tiling feature can be reached at http://www.malinc.se/m/ImageTiling.php.  Give it a try!

OK, that’s it.  I am off to play some more.

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