A mathematical formula to decipher cauliflower-type morphologies

Posted By News On December 19, 2012 - 3:00pm
A mathematical formula to decipher cauliflower-type morphologies

The cauliflower-type morphologies were known is this realm in an empirical way, but no one had provided a model like the one that these scientists have developed. "In our case," they comment, "the connection came about naturally when a certain ingredient (noise) was added to a related model that we had worked on previously. When we did that, in the numeric simulations, surfaces appeared, and we quickly identified them as the ones that our experiment colleagues had been able to obtain, under the right conditions, in their laboratories."

Based on the characteristics of this theoretical model, they have inferred general mechanisms that can be common and can help in making models of other very different systems, such as a combustion front or a cauliflower like the ones that can be found in any supermarket.

Fractals of this type are interesting because they are ubiquitous, that is, they appear in systems that vary widely in their nature and dimensions. In general, fractals can be found in any branch of the natural sciences: mathematics (specific types of functions), geology (river basins or the outline of a coast), biology (forms of aggregate cells, of plants, of the network of blood vessels...), physics (the growth of amorphous solid crystals or the distribution of galaxies), chemistry (the distribution in space of the reagents of chemical reactions).

Moreover, they have also been studied due to their relationship with structures created by man, such as communication and transportation networks, city layouts, etc.

This finding may help to discover concrete applications for improving the technologies used in thin film coatings, and to understand the conditions under which they are smooth or have wrinkles or roughness. "This is also useful in generating textures in computer simulations," the researchers point out. "And, conceptually," they add, "this can give us clues about the general mechanisms involved in forming structures in areas that are very different from the ones in which the model was formulated, such as those in which there is competition for growth resources among the various parts of the system."

This is a cauliflower.(Photo Credit: Carlos III University of Madrid )

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