Spirals are common in nature. We’ve all admired the beautiful spirals that occur on sea shells, we can find spirals in plants, and even in the arms of galaxies or weather patterns. There are also situations in which spirals aren’t a result of slow growth, but occur spontaneously in biological or chemical systems. A famous example from chemistry is the Belousov-Zhabotinsky (BZ) reaction: when several chemicals are mixed together in a petri dish, the resulting solution forms changing spiral patterns. In biology a particular slime mould, called dictyostelium discoideum, gives rise to similar patterns. Spontaneous spiral wave formation in such systems can be reproduced and studied with simple mathematical models known as cellular automata.

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Charles Darwin’s theory of evolution by natural selection is one of the most profound scientific theories to have ever been developed. However, there were several questions about evolution that Darwin himself could not answer. Not that he wasn’t smart enough (in fact, his intuition often pointed in the right direction), but the answers to those questions required sophisticated mathematical insights that were not developed far enough, or even available yet, in Darwin’s time. One such problem was the evolution of altruism. If evolution by natural selection is all about competition and survival of the fittest, how can altruistic behaviour (which, by definition, lowers the altruist’s fitness and increases the receiver’s fitness) ever evolve?

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Evolution is still all too often (but wrongly) downplayed as “just a theory” in public discussions. This is partly due to an unfortunate misunderstanding of what a theory means in science, as opposed to its common language meaning. Evolution by natural selection is much more than just a hypothesis, and is as much a valid and well-accepted scientific theory as the theory of gravitation. What Darwin did for biology is on par with what Newton did for physics — and mathematics plays an important role in both theories.

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Last night a rare event happened: the summer solstice and a full moon at the same time. So I went up Kahlenberg, a hill above the city of Vienna, to have a good view of this special full moonrise. Unfortunately my cheap little point-n-shoot camera is almost useless in low-light conditions, but I got a few halfway decent shots anyway. Click each pic to see a larger version.

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I’ve made a short movie showing autocatalytic sets arising in a dynamical simulation of a simple polymer model. It shows how autocatalytic subsets appear, one after another, and then grow in concentration. This provides a nice visual and dynamical example of our usually more graph-theoretical analyses. Continue Reading

A key result of last year’s UN climate change conference in Paris is that we now have a new international deal to curb climate change. However, it seems primarily focused on reducing greenhouse gas emissions to limit global warming. A significant step forward, no doubt, but it does not address the more difficult, and perhaps also more relevant question of how to deal with the inevitable consequences of climate change. Are we able at all to predict what those consequences will be? And, more importantly, will we be able to do something to reduce, or even prevent, some of these consequences? When it comes to biodiversity and the distribution of species, some researchers believe this is indeed possible.

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