L world (September 2009)

Everyone knows that fern is a "fractal". Another question is what that exactly means ... I've known for a long time about the rewriting algorithms used to create deterministic, but also partly stochastic objects (depending on whether in rewriting from the generation to generation one makes "mistakes"). Yet, only recently I have started to code these algorithms with the idea to make some plant or building, whatever comes out. Among the more famous rewriting algorithms are L-systems, named after Aristid Lindenmayer who "invented" them when studying the geometry and growth of algae. The idea is to represent the shape as a string that is obtained iteratively from the starting, root string, applying to all of the letters of the string certain rule (e.g. A => AB, and B => ABA or something like that). Depending on the set of rules one can obtain systems (strings) that look "biological" (of course, in a sufficient, and sometimes even strictly set number of iterations). More details can be found in Prusinkiewicz's book The Algorithmic Beauty of Plants, and I can also recommend papers and other material from the web pages of his laboratory.

At the end of experimenting, I am not too enthusiastic about all that. There are better ways to numerically (algoritmically) form a tree, plant, or a building. Compare, for example, the simulations with the "real" fern on the photograph below.

But... What exactly means that life is ordered according to mathematical and physical laws? Does that mean that behind whole Universe there is a reason similar to ours whose intentions we can understand therefore, or that mathematics and physics are nothing more than the best way to most easily fit the immense variety of the Universe to the material organization of the human brain? Maybe it is only a petty and impure resonant sound of the untuned instrumet, the sound we call mathematics. Perhaps nothing deeper is there. (from Problem promatrača (Problem of the observer))

Who knows about crithmum (motar)?. Interestingly, not many people know the answer to this question, and it is possible that I also only quite recently learned about it. It is a plant (on the photographs above) that is I guess on every rock, at least on the Croatian side of Adriatic sea. The latin name is Crithmum maritimum, and according to Wikipedia, it grows also in a cold England. It is even more interesting that crithmum is edible, so the whole information acquires value that surpasses the joy of academic discussion. Crithmum is interesting because one can see iteration in the formation of its flower that is also characteristic for the L-systems. Namely, the crithmum flower could be described as flower = c_crithmum{c_crithmum{torus}}. Here, c_crithmum is a procedure that distributes the elements in a circle of radius e.g. 10*radius_of_the_element so that they do not collide (one could also add cylinder-stalks that bind the element together by anchoring them to the point below the center of the circle). Anyhow, here is how crithmum looks like in one of the possible constructions of reality (beware, this is not a crithmum). The image was made, similar as the fern, by forming L-grammar that represents crithmum, i.e. by a direct application of the formalism of L-systems to the "present case" (+ the interpretation of the string i.e. a visualization of the "word").

<< Sea cave

Igniting the clouds >>

Last updated on 06th of September 2010