Fractals

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 coastlines 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.

self-similar

This is known as the Sierpinski triangle.

Fractals were discovered in 1975 by a scientist names Benoit Mandelbrot.

because in fractal coding you save Coefficients of image blocks instead of values of block pixels. decoding starts from initial image and Coefficients applied on it. so the initial image can have any resolution

Design computer textiles and graphics. Dot matrix was the first type of computer graphics

It is sqrt(6^2 + 5^2) = sqrt(36+25) = sqrt(61) = 7.8102, approx.

You can't have a complementary antonym for a noun. For example, could you tell me what the antonym for 'cat' is? And please don't say dog.

There is no minimum number - it is simply not possible.

Given any n points in 2-dimensional space, it is possible to find a polynomial of order (n-1) that will generate a curve going through each of those points. There are other functions which will also do the trick. So, given any number of points, it would be impossible to determine whether they were generated by a fractal or a polynomial (or other function).

1975

true

Cantor Dust

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 rearranges 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.

-- The shoreline of any coastal land is a fractal.

-- The distant view of any mountain range is a fractal.

-- Your eyes perceive changes in light brightness on a logarithmic scale.

-- Your ears perceive changes in sound loudness on a logarithmic scale.

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.

The Julia can be generated by a quadratic equation in the complex plane. Select a complex number c. Then for a point z in the plane, carry out the iteration,

zn+1 = zn2 + c.

Colour-code the point according to how many iterations are required before its magnitude exceeds any given threshold. Repeat for all z in the region of the plane.

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 and 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.

Personally i would buy the Arbor Axis Koa because its a much smoother ride but its for advanced riders so if its your first longboard its going to be so much easier to learn on the Sector 9 fractal but it all comes down to your personal preference!!

Koch Curve

APEX :)

You can never draw a fractal because it is an infinitely replicating pattern. Unlike the decimal representation of a number, for example 1/3 where you can put a dot over the 3 to indicate the fact that the digit recurs infinitely many times, there is no short-cut available for fractals.

To draw an approximation of a fractal, you start with some pattern in mind. You then replace some parts of the original pattern by similar but smaller versions of the pattern. Repeat again and again until the end of time - and beyond!

Sierpinski's Triangle

Sierpinski's Carpet

The Wheel of Theodorus

Mandelbrot

Julia Set

Koch Snowflake

...Just to name a few(:

They were first studied in the 17th century by Leibniz.

ungaluke theriyala enaku epudi theriyum.

Complex mathmatic equations.