By: William Brown, Biophysicist at the Resonance Science Foundation

A chaotic dynamics is typically characterized by the emergence of strange attractors with their fractal or multifractal structure. On the other hand, chaotic synchronization is a unique emergent self-organization phenomenon in nature [1].

Complex systems are, by their intrinsic nature, immensely challenging to describe and delineate scientifically. Of particular interest in understanding their uniquely chaotic behavior is how synchronization and self-organization emerge from such systems, as is often observed [2,3]. For instance, synchronization underlies numerous collective phenomena— providing a scaffold for emergent behaviors— ranging from the acoustic unison of cricket choruses and the coordinated choreography of starling flocks to human cognition, perception, memory and consciousness phenomena [4-6]. As the authors— a group of physicists from Bar–Ilan University in Israel—...

Image by: Arkadiusz Jadczyk

^{By Dr. Inés Urdaneta / Physicist at Resonance Science Foundation}

The word fractal has become increasingly popular, although the concept started more than two centuries ago in the 17th century with prominent and prolific mathematician and philosopher Gottfried Wilhelm Leibnitz. Leibnitz is believed to have addressed for the first time the notion of recursive self-similarity, and it wasn’t until 1960 that the concept was formally stabilized both theoretically and practically, through the mathematical development and computerized visualizations by Benoit Mandelbrot, who settled on the name “fractal”.

Fractals are defined mainly by three characteristics:

1. Self-similarity: identical or very similar shapes and forms at all scales.
2. Iteration: a recursive relationship limited only by computer capacity. With sufficiently high performance, the iterations could be infinite. This allows for very detailed shapes at every scale, that modify...