FRACTALS & CHAOS

FRACTALS & CHAOS

I have always been attracted by the idea to describe nature by using mathematical equations. The concept that maths is not just a man-made construct, but it could be embedded in the ‘natural’ occurrence of time and matter, has always been promoted by scientists of all kinds. Only recently, though, due to the work and active communication of Prof. Benoit Mandelbrot (and his predecessors, Fatou and Julia, to name a few), a new mathematical theory and related objects further filled the gap between mathematics and nature.

Fractals are geometrical shapes with dimensions that go beyond the classic Euclidean classification (0: point, 1: line, 2: plane, 3: solid). They fill the space with fractional dimensions (e.g. 1.6), meaning tha they can occupy more than a line (1) but less than an area (2). In biology, this is the way the bronchial tree, the vessel ramification, and the neuronal branching work.

Another important aspect is that what we observe at a large scale can also be observed at a smaller scale (self-similarity), and this process repeats at all magnification levels. Again in the biomedical domain, we can expect that in a geometrically fractal structure, also the processes could behave similarly at many levels of temporal magnification.

the Beauty of Mathematics

The pictures in this page were created more than 20 years ago by using my MacII and Microsoft BASIC. Mathematics was the simple part, while the rendering was certainly a challenge.

The addiction driving my interest and activity in this direction was the possibility to ‘create’ artificial mountains, lakes, tree, forests and a complete set of beautiful, very convoluted objects that witnessed not just the power of maths, but how far from a cold discipline it is.

Computer power at that time was very low about 1 MHz) and it took sometimes about a week of continuous processing to obtain the complete picture.

Among the artificial objects there were Mandelbrot and Julia sets, in 2d and 3D (actually in 4D quaternions, then the result was sliced down one dimension), Graftals, Logarithmic Spirals, Chaos scene from the Standard Map).

After having displaied my pictures at two exhibitions on ‘Fractals and Chaos Geometry’ in Milan (1988 and 1991), I also wrote programs generating fractal sequence of notes via MIDI interface (demonstration presented in Rocella Ionica, 1993).

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