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What is it difference between complexity theory and chaos theory in computing and algorithms?
Does complexity theory equal chaos theory?
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The short answer is no, but......what often appears as chaos is sometimes simply complexity we haven't met yet. Sometimes more accurate systems of measure of initial conditions may nudge a chaotic system into the complex realm. But there is a distinct difference between complexity theory and chaos theory and a difference in the computations and algorithms used and continuing to evolve.
Both theories and their related equations , computations, and algorithms are used to study systems that are non linear in nature. Uncertainty is a major characteristic of both chaotic and complex systems. The nature and origin of the complexity is the key difference between chaos and complexity.
Note that the term “edge of chaos” gets used quite a bit in scientific and science fiction writing. Confusing the matter, this term is normally associated with complex systems. "The Edge of Chaos" represents a point that sits along a spectrum. On one end is determinism and on the other is not chaos per se, but randomness. The edge of chaos begins where there is sufficient observable structure / patterns in the system that it is not random, but also enough fluidity and emergent creativity that the system is not deterministic.
Patterns are an important,and often repeating element in complex systems despite the fact that complex systems have inherent uncertainty. With sufficient observable patterns and structure future actions, changes, within a complex system are not random, but fall within a predictable range of possibilities. Complex systems are never "one right answer" systems they are nonlinear non-Euclidean. In the hey day of classical (Euclidean) math they were a source of great controversy. (See my post "August 10, 1632 THE BATTLE OVER THE "INFINITESIMAL" ) The emergence of complexity theory demonstrates a domain between deterministic order and randomness which is complex. Complexity Theory did emerge from Chaos theory but it does not eclipse Chaos theory. Chaos is sometimes perceived as extremely complicated information rather than an absence of order. Chaotic systems, in contrast to complex systems, remain deterministic. Their long term behavior can be practically impossible to predict with any accuracy.
When one engages in analysis of complex systems,sensitivity to initial conditions , if even knowable, is not as important as within systems contained in Chaos Theory. Initial conditions are a primary consideration within Chaos systems where sensitivity to initial conditions, prevails as a deterministic element.
.In Conclusion, it can be tempting to think of of Chaos theory as a theory of highly complex types of complex systems. But that is not the case Chaos theorists have contributed some key insights of complexity, like sensitivity to initial conditions, but Chaos Theory remains a study of deterministic systems. To understand non-deterministic systems, like ant colonies , or markets, it’s necessary to look at complex systems and Complexity Theory.