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It is shown that the resulting three dimensionality rests on two factors which have been hitherto ignored, viz., a Machian or holistic property and the stochastic underpinning of the universe itself.
However the dimensionality is scale dependent in the sense that at very large scales, or at very small scales, we encounter a different dimensionality, as indeed is borne out by observation and experiment. ....Finally it is shown how fractal dimensions can emerge....

http://en.wikipedia.org/wiki/Stochastic
Stochastic, from the Greek "Στόχος" which means "aim, guess", means of, relating to, or characterized by conjecture and randomness.
A stochastic process is one whose behavior is non-deterministic in that a state does not fully determine its next state. Stochastic crafts are complex systems whose practitioners, even if complete experts, cannot guarantee success. Classical examples of this are medicine: a doctor can administer the same treatment to multiple patients suffering from the same symptoms, however, the patients may not all react to the treatment the same way. This makes medicine a stochastic process.
Additional examples are warfare and rhetoric, where the successes and failures cannot be certainly predicted.
Mathematical theory
In mathematics, specifically in probability theory, the field of stochastic processes has for some decades been a major area of research.
A stochastic matrix is a matrix that has non-negative real entries that sum to 1 in each column.
Artificial intelligence
In artificial intelligence stochastic programs work by using probabilistic methods to solve problems, as in simulated annealing, stochastic neural networks, stochastic optimization, and genetic algorithms. A problem itself may be stochastic as well, as in planning under uncertainty. A deterministic environment is much simpler for an agent to deal with.
Natural science
An example of a stochastic process in the natural world is pressure in a gas as modeled by the Wiener process. Even though (classically speaking) each molecule is moving in a deterministic path, the motion of a collection of them is computationally and practically unpredictable. A large enough set of molecules will exhibit stochastic characteristics, such as filling the container, exerting equal pressure, diffusing along concentration gradients, etc. These are emergent properties of the system.
Biology
Stochastic resonance (see oscillators)
In biological systems, introducing stochastic 'noise' has been found to help improve the signal strength of the internal feedback loops for balance and other vestibular communication. It has been found to help diabetic and stroke patients with balance control.