Fractals

Well, let's take a moment to appreciate the beauty of simplifying fractions. If we divide both 36 and 126 by their greatest common factor, which is 18, we get 2 over 7. Just like that, we've simplified the fraction and created a little masterpiece of math!

Counting the whole square as iteration 0, there are 46 = 4096 segments after iteration 6.

They show self-similarity. When you look at a more detailed (or zoomed-in) version of the fractal you have the same image.

No, it is not.

put your pencil to the paper and begin drawing a line, and never stop... (you are going need an infinitely large sheet of paper)

* * * * *

You do not need an infinitely large piece of paper. But you will need infinitely many pencils and an infinite amount of time!

Traditional geometric figures have dimensions which are integers: 0 for a point, 1 for a line or Mobius strip, 2 for a plane figure or Klein bottle, and 3 for a solid. Fractals have dimensions which are not integers.

Fractal Analytics was created in 2000.

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)

I would suggest using a 3d printer and thingiverse.

your dad

There is an element of fractal property in the manner in which an artery divides into smaller vessels and these in turn to still smaller vessels and so on until you reach capillaries. And then, you have the reverse process of capillaries joining together to form veins which join up to form larger veins and so on. Many branching processes are approximately fractal.

By their very nature fractals are infinite in extent.

Maple leaf, peacock

7.4

Yes.

Crystals are usually not fractals.

When the middle third of a line segment is removed and repeated infinitely on the resulting line segments the result is the Cantor Set.

When shifting to 2 dimensions, starting with a triangle, dividing it up into 4 similar smaller triangles and removing the middle triangle results in the Sierpinski Gasket; the limit of colouring Pascal's triangle with the even numbers as black and the odd numbers as white, as the number of rows tends to infinity is the Sierpinski Gasket.

Shifting to 3 dimensions, starting with a cube, dividing it up into 27 smaller cubes and removing the middle cube of each face and the centre cube results in the Menger Sponge.

The Sierpinski Gasket and Menger Sponge are 2 and 3 dimensional analogues respectively of the Cantor Set.

It need not affect it in any way whatsoever.

yes i think so because a fractal is an object that is self-similar

all squares are similar; so are all cubes

Numbers are not fractal so it is not possible to answer the question.

They can be three dimensional, for example, the Menger Sponge. Mathematically, there is no limit to the number of dimensions.

The concept of fractals can be traced back to mathematicians Benoit Mandelbrot and Georg Cantor. Mandelbrot is often credited with popularizing the term "fractal" and demonstrating their applications in various fields.

In social studies, an upside down triangle could represent a pyramid of power or social hierarchy, where those at the top have the most power or authority and those at the bottom have the least. It can be used to visually represent societal structures and relationships.