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Chaos theory and the butterfly effect The definition The purpose

Mathematical Fractals The definition The Artwork The creation

Chaos theory is a field of study in mathematics, physics, and philosophy studying the behavior of dynamical systems that are highly sensitive to initial conditions.

In dummy words… The chaos theory is the thought that the

future depends on the smallest things we do right now.

What we do right now will spark a significant reaction years from now

The butterfly effect is a metaphor that encapsulates the concept of sensitive dependence on initial conditions in chaos theory; namely that small differences in the initial condition of a dynamical system may produce large variations in the long term behavior of the system.

In dummy words The butterfly effect is another word for the act

of something small creating a huge change in a set future. It only exist if the chaos theory is more than a theory.

The purpose of the study of these two related theories is to ultimately be able to undoubtedly predict the future events based off of actions being made presently. It can also be used to reveal hidden portions of the past through the effects that happened later on the road.

A fractal is "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

In dummy words… Fractals are shapes that can be split apart,

which makes a smaller copy of the original shape

Escape-time fractals – also known as "orbits" fractals) These are defined by a formula or recurrence relation at each point in a space (such as the complex plane). The 2d vector fields that are generated by one or two iterations of escape-time formulae also give rise to a fractal form when points (or pixel data) are passed through this field repeatedly.

Iterated function systems – These have a fixed geometric replacement rule

Random fractals – Generated by stochastic rather than deterministic processes

Strange attractors – Generated by iteration of a map or the solution of a system of initial-value differential equations that exhibit chaos

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