Trip Into Infinity

A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity. The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured." A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.
A fractal often has the following features:
•It has a fine structure at arbitrarily small scales.
•It is too irregular to be easily described in traditional Euclidean geometric language.
•It is self-similar (at least approximately or stochastically).
•It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).
•It has a simple and recursive definition.
Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms).



Binaural beats or binaural tones are auditory processing artifacts, or apparent sounds, the perception of which arises in the brain independent of physical stimuli. This effect was discovered in 1839 by Heinrich Wilhelm Dove.
The brain produces a phenomenon resulting in low-frequency pulsations in the loudness of a perceived sound when two tones at slightly different frequencies are presented separately, one to each of a subject's ears, using stereo headphones. A beating tone will be perceived, as if the two tones mixed naturally, out of the brain. The frequency of the tones must be below about 1,000 to 1,500 hertz for the beating to be heard. The difference between the two frequencies must be small (below about 30 Hz) for the effect to occur; otherwise, the two tones will be heard separately and no beat will be perceived.
Binaural beats are of interest to neurophysiologists investigating the sense of hearing. Second (and more controversially), binaural beats reportedly influence the brain in more subtle ways through the entrainment of brainwaves and can be used to produce relaxation and other health benefits such as pain relief, synchronization of the brain hemispheres and activation of the right hemisphere which we don't use it as much as the left one.