Probing the edge of chaos: How do variable physical characteristics behave at the point preceding onset of chaos?

In probability theory, the central limit theorem was first developed by an 18th century French mathematician named Abraham de Moivre. It applies to independent random physical quantities or variables, each with a well-defined expected value and well-defined way of varying. This theorem states that once iterated a sufficiently large number of times, these variable physical quantities will be approximately distributed along a central limit-also referred to as the attractor. In chaotic and standard random systems, such distribution is in the shape of a bell curve.

Now, new central limit theorems are emerging for more complex physical processes, such as natural phenomena. In this study, the authors took existing knowledge of the specific position of the attractor at the edge of chaos. To do so, they employed a mathematical formula called the logistic map as a particular example of the dynamic system under study. They found that the distribution of physical properties of such dynamic systems at this specific point at the edge of chaos has a fractal structure not previously known.