To continue on "patterns which don't need a creating intelligence":

Quote:

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In 1984, George Cowan organized a research group called the Santa Fe Institute, assembled to study what could be one of the most fundamental theories about the nature of our world’s complex systems, and the unifying principles that bind them. Though following relatively simple basic principles, the structural complexity of ant colonies is remarkable. World economies, with individual agents acting in limited capacity, produce exclusively macro-level behavior. The neuronal mess of the human brain produces concepts so liquid and elusive as thought, and consciousness, with no apparent or conceivable physical, cognitive correlate. The most core of these principles is this: that these seemingly inexplicable complex systems manage to form from relatively simple rules and initial, guiding principles. It is inconceivable, yet tempting, and subtle despite ubiquity.

Related to (but distinct from) complexity theory is chaos theory, which explains that small change in initial conditions can bring about dramatic, seemingly disordered effects. This is the theory that brought Edward Lorenz, in 1961, to coin the term “the butterfly effect” (the situation of a butterfly flapping its wings, and that slight effect it creates potentially generating a tornado that otherwise would not have been). Basically, many phenomena are impossibly unpredictable. They are completely chaotic, seemingly random. But, the very fact that a change in initial conditions (sometimes as small a change as a 4th decimal place for an initial value, or smaller) can bring about new results does show a degree of causality.

Chaos theory was developed in large part by Benoit Mandelbrot, who created the term “fractal”. A fractal is a self-similar geometric phenomenon, irregular but with a familiar and consistent pattern. Self-similarity refers to the property whereby no matter how much you zoom into an image, the same fractal pattern is represented. Or, rather, that the figure’s general theme/shape is composed of a number of instances of that exact same theme/shape, and these individual composing pieces are themselves composed of the same number and configuration of parts as the level above. Fractals are generated mathematically, through the use of specific types of self-referential equations. A small change in the initial conditions of a fractal generation produces vastly different large-scale results for the final picture.

Since their discovery, fractals have since been found throughout nature, in swirling seashells, electric bolts, types of broccoli, and are the most accurate description of the trace of coastlines. Fractal mathematics have been used to create complex and often beautiful works of art. The property of self-similarity produces hypnotic swirls, maddening designs of infinite, swallowing complexity.

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This is a quotation from this site: http://www.thehumanpurpose.com/

I don't know what's this "human purpose" is about, please ignore it.
What I know is that the quote does explain quite well in short words what this self-referential system is about. Hope, that you can understand it, even if you didn't know much about that before...

EDIT(it is still too complicating, I try to explain it a bit better):
The main thing is this:
"Fractals are generated mathematically, through the use of specific types of self-referential equations."
The equations are called self-referential because there is a row of equations with the same form and same constants, BUT the result of the first of the row is placed into the second within the row via the variable, and the result of this equation is placed into the third of the row and so on...
This is compared to time, the row is imagined as the time, so each part of the row is a step within the time, the constants are constant conditions, and the results are representing the changes within the conditions.
And, if the changes within these conditions build patterns, then you can speak of a system.