Video3

**Video 3: Fractals **
 What’s a fractal? If you do not know, please look it up in a dictionary, copy it and acknowledge the source.
 * Before watching **

(A) **Fractal** is a semi geometric object of which basic structure, fragmented or irregular, is repeated on different scales. The term comes from the Latin word fractus, which means broken or fractured. Many natural structures are fractal-type. http://maria-alejandra-fernandez.wikispaces.com/My+Glossary

Give an example of a fractal

A class of examples is given by the [|Cantor sets], [|Sierpinski triangle] and [|carpet], [|Menger sponge], [|dragon curve], [|space-filling curve], and [|Koch curve]. Additional examples of fractals include the [|Lyapunov fractal] and the limit sets of [|Kleinian groups]. Fractals can be __[|deterministic]__ (all the above) or[|stochastic] (that is, non-deterministic). For example, the trajectories of the [|Brownian motion] in the plane have a Hausdorff dimension of 2. []

Mention five words you think you might find in this video about fractals Fractal Geometric Formula Structure set

Please click on the following link to watch the video. []
 * During and after watching **

1. Listen carefully to the video to see if you can find the words you wrote in the question above. List them: Fractal, Geometric and structure.

2. What is a fractal?

A fractal is an object which irregular form repeats itself from the most wide vision of the figure even the most microscopic vision of the figure, that is to say, the irregular forms of the figure repeat themselves to a smaller and smaller scales.

3. What are its properties? Explain them

I understand that the first property is "the fractal have structures goes all the way down", but I'm not sure that it mean, and the second property is "the small features resemble the larger ones", in this sense, the structure could be set to be a self similar.

4. Mention some examples of Euclidean shapes. Are they fractals? Why?

Some examples of Euclidean shapes are circles, squares and spheres. The Euclidean shapes are non-fractals, because when we extend a part of one of these shapes (we take smaller segments), this segment of the shapes tends to be a straight line, that is to say, is not kept as a copy of the biggest segments. Therefore the Euclidean Shapes are not consistent with the first property of the fractals.

5. What is self similarity?

The self similarity is a kind of simmetry.

6. Is the Romanesco broccoli a real fractal? Why?

The Romanesco Broccoli is a fractal vegetable (a natural fractal or a fractal product of the nature), but in theory, the Romanesco broccoli is a partially fractal, because the repetition of structure is not perfect and the replication may not be perfect. This vegetable is a kind of flower formed by cones that to the same time have smaller cones and these cones have smaller cones, so this is consistent with the second property of a fractal.

7. How would a mathematician describe symmetry?

An object has a symmetry if it stays the same despite a change.

8. What kind of symmetry do fractals have? Please define it.

The fractal has a scale symmetry. The scale symmetry means that the object stays the same despite a scale change.

9. How is fractal geometry part of chaos theory and/or viceversa?