What are fractals?

Definitions:

**Fractals**: A geometric pattern that is repeated (iterated) at ever smaller (or larger) scales to produce (self similar) irregular shapes and surfaces that cannot be represented by classical (Euclidian) geometry. Fractals are used especially in computer modeling of irregular patterns and structures found in nature.

Can science be beautiful? What is beauty? Can anything which is classified by cold, hard facts and governed by fixed equations be beautiful? *Why* are facts considered cold, hard (except to Scientists)

Take a look at various fractals.

The “ Mandelbrot “ pattern, various fractals are generated using programs which really appeal to us. Various programs create beautiful symmetrical *and *asymmetrical patterns which are extremely attractive.

Crackers, certain decorative chemical reactions, various computer generated reactions, even the concept of beauty as perceived by humans has been studied as a science. Various phenomena (such as the auroras), involving physics are breathtaking.

Indeed, can *anything* be separated from science? Is there any such thing in the world that cannot be quantified, observed, *studied*?

Various phenomena that scientists *have *observed have been carefully studied, quantified and noted down. Occasionally the phenomenon is even mathematically modeled before the actual science *behind* the phenomenon has been discovered/observed/understood. Case in point: Quantum Physics: the behavior of photons, and all mass for that matter. Philosophy, which used a term encompassing all science, as we know it today has been drastically reduced to only certain areas, is still part of physics. …

“Does the act of observation change the object being observed? Does anything actually exist and have properties or are the properties a result *of the act of observation? *Does a falling tree in the forest make a sound *if there is no-one to hear it*? This also corresponds to the beliefs of many religions.

Can any area of study be completely independent of all other areas? Can anyone gain a complete perspective on a certain subject without knowledge of other subjects related to it? Can a *single* *person* obtain the *complete* picture of any object in a single lifetime? Would not the complete and absolute knowledge of a *single* object involve knowledge of *everything that exists* because everything is in some way or the other related?

Perhaps what expresses this all in words that are simple and yet beyond me is an excerpt from Elton John’s

*The Circle of Life :*There’s more to see than can ever be seen

*More to do than can ever be done*

There’s far too much to take in here

More to find than can ever be found

And all we can do is to learn as much as we can. To study, and to perhaps understand a fragment of the world we live in; to *really* understand the *why*, the *what*, the *where. *The task is formidable. Perhaps Terry Pratchett expressed this best in *Lords and Ladies*:

..” the agonized expression of a man who has the whole great whirring machinery of the Universe to dismantle and only a bent paper clip to do it with.”

All of us are in the same situation. All of us have our own universes to decipher, to dismantle, to analyze. In addition, most probably, *none *of us will succeed.

Nevertheless, we will all *try*. Because we are *human*. Because we are* curious*. Because we are *alive.*

However, most of all, because we *play chess…. Ok, think.. Same difference ?!*

From Wikipedia, the free encyclopedia

Frost crystals formed naturally on cold glass illustrate fractal process development in a purely physical system

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,"^{[1]} a property called self-similarity. Roots of mathematically rigorous treatment of fractals can be traced back to functions studied by Karl Weierstrass, Georg Cantor and Felix Hausdorff in studying functions that were continuous but not differentiable; however, the term *fractal* 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.^{[2]}

A fractal often has the following features:^{[3]}

Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms). Natural objects that are approximated by fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, snow flakes, various vegetables (cauliflower and broccoli), and animal coloration patterns. However, not all self-similar objects are fractals—for example, the real line (a straight Euclidean line) is formally self-similar but fails to have other fractal characteristics; for instance, it is regular enough to be described in Euclidean terms.

Images of fractals can be created using fractal-generating software. Images produced by such software are normally referred to as being fractals even if they do not have the above characteristics, such as when it is possible to zoom into a region of the fractal that does not exhibit any fractal properties. Also, these may include calculation or display artifacts which are not characteristics of true fractals.