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In Geometry

Fractals can be generated with computer programs like Sterling or Apophysis. Both of these are freeware you can easily download. There are other programs, like Ultra Fractal a…nd Tierazon, as well. With Sterling, you are given a default fractal that you can transform using various modes, and then zoom in and search for a good design. With Apophysis, you are given a set of randomly-generated "flames" that you can transform using various "plug-ins", some of which are included in the download, others can be downloaded free. Apophysis flames are can be edited by manipulating the triangles that define it. Each triangle can be manipulated using plug-ins such as "spiral." Several tutorials are on the Internet, at places like deviantart.com, which has groups liked I linked below. An example of fractals generated with Sterling and Apophysis can be found in a gallery I also linked below. (MORE)

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In Geometry

Benoit Mandelbrot is the man who is usually credited to have discovered fractals in the year 1975. He was the first person to use this word and was also the first man to repre…sent them in visual form. But history also shows that some facts about fractals were known to mathematicians as early as the 17th century. (MORE)

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In Geometry

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 (self similar). 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. (MORE)

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In Technology

Seperation of atomic structures including but not limited to non biological elements such as stone, rock, even water. It induces a weird sort of decay which literally rearrang…es atoms at times to form something completely different... different atoms, different structures and different material. In short, everything or any thing melts, moves or explodes at room temperature or at widely various temperatures and pressures. Interesting as it can be,although it is a form of sound, it reacts to other elements as vibrations like heat without being hot. Even better, add magnetism and/or eletricity and you will get a completely different reaction such as levetation, erratic movements and even swift-vertical alignment or stationary rotation of certain materials. Like a phenomenon this is a freak of nature which contradicts most theories. It also can promote, prompt, and sustain an unknown form of self healing within the human body, "regeneration" where damaged cells are some how replaced, not repaired, replaced. Multiple fractal nonlinear resonance devices and frequencies can be applied in multiple directions and yet again, you will get a completely different result. These results are complex and vary greatly depending upon all applied forces such as the number of devices, number of personel present, direction of each device, moisture/ humidity, atmospheric pressure, any additional sounds/pressure waves including speech and independent/external sources such as traffic, amplification vs. de-amplification, state of matter, amount of matter and even the presence and position of what I thought were non relevant items/material that were not a direct target. It is astonishing yet a beautiful reality. (MORE)

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In Geometry

a curve or geometric figure, each part of which has the same statistical character as the whole. Fractals are useful in modeling structures (such as eroded coastli…nes or snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth, fluid turbulence, and galaxy formation. (MORE)

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In Geometry

Benoît B. Mandelbrot[ is a French mathematician, best known as the father of fractal geometry

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In Geometry

Examples of fractals in everyday life would be for example a fern. A fern is a type of leaf with a certain pattern. This pattern is the fractal because as you zoom in on the f…ern the pattern remains the same. It is the same thing over and over again no matter how far you look into it. This happens because of the fractal dimension. (MORE)

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In Geometry

Fractals are generated from recursive mathematical equations, this is why you can zoom-in on them infinitely and they will continue to repeat themselves (this is also why they… are so computationally intensive) (MORE)

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In Geometry

It really depends on the fractal, and there are many possible ways to define them. As an example, for the Mandelbrot set, a number of calculations involving complex numbers ar…e done for each point in the complex plane, to determine whether a point is part of the set or not. However, other definitions are possible as well. (MORE)

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In Fractals

Some examples: a coastline, the tributaries of a river, a branching tree, a snowflake. Some examples: a coastline, the tributaries of a river, a branching tree, a snowflake. … Some examples: a coastline, the tributaries of a river, a branching tree, a snowflake. Some examples: a coastline, the tributaries of a river, a branching tree, a snowflake. (MORE)