Tree of life / Az élet fája
Our project is based on two foundations: one is fractals in general and the other is the so-called L-system, or Lindenmayer-system. Fractals can be briefly defined as "a pattern or shape of which any part can be regarded as the same as the whole". This means that if you zoom in on a small part of a fractal, you will get essentially the same shape over many enlargements. This can of course not only be seen at a mathematical or geometric level, but also in sound effects, for example.
Fractals are usually described by various mathematical models. One of these is the Lindenmayer-system mentioned above. It was originally developed mainly to model plant growth and was also used to describe the division of different plant cells (as the title of our project - Tree of Life - shows, plants themselves exhibit fractal features), but it is now used to describe many similar fractal structures, including the branching of vascular networks in organs such as the lungs and kidneys, to name but a few.
The essence of the Lindenmayer-algorithm we use is as follows:
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there is an alphabet for the algorithm: this is the set of possible characters that can be inserted into a "sentence". For example, if the alphabet is "ABC", then each "sentence" contains the three characters A, B and C, and only these.
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There is a starting "sentence" which defines the initial state of the system: for example, using the alphabet "ABC", the starting sentence could be: "AAA" or "B" or "ACBAB".
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rules of derivation: these are applied to the initial sentence and then applied continuously to newer and newer sentences, generating newer and newer sentences. An L-system rule contains two sentences, a "predecessor" and a "successor". For example, with the rule "A → AB", whenever an "A" is found in a string, it is replaced by "AB".
Illustration of the sentence system - you can see how successive generations are formed.
From the first generation, we can determine the subsequent generations: for example, the branching system of a tree.
As emphasised earlier, fractals occur in many parts of the living world, from the structure of plants, through the formulas found in human and animal organisms, to the world of unicellular organisms. Focusing on the Lindenmayer system, and the human body in particular, our presentation aims to capture its beauty and regularity.