John Robinson's sculpture "Temple of Fire" is analogous to a construction already found in mathematics by W.Sierpinski in 1915.
The Polish mathematician Wraclaw Sierpinski died in 1969. His grave bears only these words:

Explorer of the infinite.

Sierpinski 'Cheese'
1st iteration

Note that, unlike Robinson's sculpture, the right hand picture does not involve any upside down tetrahedra, and that regular tetrahedra are used instead of elongated tetrahedra.

Fractals: at the infinite limit of a process of iterations.

Sierpinski's aim was to consider iteration, i.e. repetition, of the above process, so that each small tetrahedron of the first iteration is replaced by the first iteration:

The fractal is the "limit" of this process. It is an extraordinarily complicated object with a strong property of self-similarity. These ideas are easier to explain in the 2-dimensional analogue, the Serpinski gasket, which was found first.

Note that the whole figure can be found again in its own details: this is true at all scales; this feature is easily understood from the process of construction.

The Sierpinski Gasket

(Click to magnify)
Robinson, without knowing of Sierpinski's work, was aware of the idea of fractals and has perceived the importance of this iterative process, as shown in his words:
" I also see it being like a Gene, because you can go on adding tetrahedra to the sculpture for ever, so that it becomes like a Family Tree. If you go back 1000 years, we each have millions of ancestors. We are the Genetic melting pots of survival Genes.".

On the left is another iteration of the process giving Robinson's sculpture :

Fractals: symbolism and life.


©Mathematics and Knots/Edition Limitee 1996
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