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Produced by Andy Burbanks
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The picture is a realisation of a recursive tree-like structure (see the movie below). There is a central drive shaft with three arms attatched. Each of these in turn has 3 of its own sub-arms, and so on through a few levels of recursion. The structure sits atop a platform inscribed with an escher-style tiling
Once the rules defining such a structure have been designed, it is modelled 3-dimensionally using some simple recursive C++ routines. The model is then rayshaded using the package Persistence of Vision (POVRAY).
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| The image to the right was previously used as a School logo for the WWW pages of the School of Mathematics. The object is called the Sierpinski Gasket and is constructed by following a simple rule repeatedly: begin with a pyramid, and at each stage replace each pyramid by four smaller copies (arranged to fit neatly inside the original), repeat the process.
Note: the picture shown differs from the usual Sierpinski Gasket, in that I have used five pyramids at each stage to give a square-base to the structure.
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The Menger sponge
Recipe
- Take one cube
- Divide into 27 smaller cubes, evenly
- Remove all the cubes that are in line with the centre of a face of the original cube (warning, this is the tricky bit! the whole structure is prone to fall apart)
- Repeat the process on all resulting cubes
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Movies
Several pictures can be combined into a movie, using the mpeg_encode package. With careful use of both C++ and shell-scripts, the whole process can be automated.
Clicking on the picture below gives a movie of the recursive propeller which demonstrates what happens to this particular structure as a parameter is varied. The parameter being changed is the angle of attachment of the arms (and thus the angle of attachment of the sub-arms and sub-sub-arms, and so on).
I have made an effort to make the object look physically realistic (although I wonder what mechanism the gold spheres would have to contain in order for this object to be constructed physically!).
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Mpeg movie
I suggest that you load the movie to your local disk and play it there in loop mode if you want to see more revolutions of the propeller.
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