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Fractals

"Fractals are mathematical constructions of fractal geometry, a relatively new geometric form only discovered/defined in the 1970's by Benoit Mandelbrot who actually coined the term ""fractal"". Previously considered mathematical ""monsters"" fractals were largely ignored by mathematicians as they behaved in ways that were difficult to describe/define, in particular they were ""monster"" curves that were non-differentiable. Benoit Mandelbrot deliberately got a job at IBM in the 1970's so he could gain access to the computing power necessary to study these objects in more detail and since his initial studies Fractal Geometry has become part of every branch of science and given rise to the increasingly popular Fractal Art medium.

429 Questions

What is fractal writing?

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Fractal writing is a technique where a writer uses repetition, self-similarity, and patterns to create a text that mirrors itself at various levels of scale. It often involves layers of meaning that unfold as the reader progresses through the text, creating a sense of complexity and depth. This technique is inspired by the mathematical concept of fractals, where complex patterns are built from simple repeated shapes.

What do Hollywood special effects have to do with fractals?

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Fractals are used for computer generated terrains.

Fractals have what familiar property?

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It is a property called self-similarity. When you zoom in to a particular part of the fractal you see the same pattern as was visible before the zoom.

What is 5 6ths times 4 5ths?

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5/6 x 4/5 is 2/3.

When was Ultra Fractal created?

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Ultra Fractal was created in 2006-05.

Are all snowflakes fractals?

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No, none of them are. Under sufficient magnification you will be seeing individual ice crystals and with any further enlargement, you will no longer have the property of self-similarity.

What is the coordinates of a rectangle with a length of 5 units and a width of 2 units?

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There is not enough information to provide an answer.

You need to know the coordinates of three vertices before you can find the coordinates of the fourth. Otherwise, there are alternative solutions using translations, reflections and rotations.

Does a rectangular prism have 4 faces that are square and 2 faces that are rectangles?

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Not necessarily. It can have 6 rectangular faces.

Which solid figures have 0 flat surfaces and 0 vertices?

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An ovoid (egg-shape) is one possible answer. A smooth blob (to use a very technical term!) is another.

What are frozen fractals?

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Is a flower a fractal?

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No, it is not.

What is Benoit Mandelbrot most well known for?

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Benoit Mandelbrot is most well known for his discovery of patterns in nature, which he termed "fractals". Mandelbrot, now deceased, was a mathematician who primarily studied advanced geometry. His "Theory of Roughness" was formed when he found infinitely repeating patterns in mountain ranges and coastlines.

Are the Torus the Vector equilibrium the Phi spiral or Fractals related?

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The Torus vector equilibrium is a vortex by which nature forms energy into matter. The Phi spiral also known as the Golden ratio is commonly found in nature. At this time there is no link between the torus vector equilibrium and the phi spiral, although a link between the two has not been disproved.

Where is it possible to view different fractal patterns?

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There are a variety of online sites which contain pictures of fractal patterns and lists of places where fractal patterns can be seen in nature. The web domain FractalFoundation, for example, provides this service.

What kind of triangle can be made in a rectangle?

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Any kind of triangle can be made in a rectangle.

What are some common techniques for generating fractals?

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Some common techniques for generating fractals would be to use iterated function systems, strange attractors, escape-time fractals, and random fractals.