Mathematicians and psychologists don't cross paths that often and when they do you wouldn't expect it to involve an (apparently) unassuming puzzle like the Tower of Hanoi. Yet, the puzzle holds fascination in both fields.
If you're bored with your holiday snaps, then why not turn them into fractals? A new result by US mathematicians shows that you can turn any reasonable 2D shape into a fractal, and the fractals involved are very special too. They are intimately related to the famous Mandelbrot set.
If, like us, you like fractals, then you will love the work of Frank Milordi, aka FAVIO. Milordi is a former Director of Engineering and Technology who creates mind challenging computer images based on the mathematics of chaos and fractals. You may be familiar with his work already, as one of his beautiful fractal images adorns one of the latest Plus postcards.
The world we live in is strictly 3-dimensional: up/down, left/right, and forwards/backwards, these are the only ways to move. For years, scientists and science fiction writers have contemplated the possibilities of higher dimensional spaces. What would a 4- or 5-dimensional universe look like? Or might it even be true that we already inhabit such a space, that our 3-dimensional home is no more than a slice through a higher dimensional realm, just as a slice through a 3-dimensional cube produces a 2-dimensional square?
Benoît Mandelbrot, the father of fractal geometry, died last Thursday at the age of 85. Born in Poland in 1924, Mandelbrot had dual French and American citizenship and spent most of his working life in the US. He died of cancer in a hospice in Cambridge, Massachusetts.
The human brain faces a
difficult trade-off. On the one hand it needs to be complex to ensure high performance, and on the other it needs to minimise "wiring cost" — the sum of the length of all the connections —
because communication over distance takes a lot of energy. It's a problem well-known to computer scientists. And it seems that market driven human invention and natural selection have come up with similar solutions.