# What is Fractional Dimension and What is a Fractal? (TANTON Mathematics)

Take a picture to a photocopier and set it to scale by a factor of three. Then all lengths in the picture triple in size (factor of three to the one-th power) and all areas increase by a factor of nine (three to the two-th power). But there are objects that scale by fractional powers!

## 9 thoughts on “What is Fractional Dimension and What is a Fractal? (TANTON Mathematics)”

1. Curixq on said:

If﻿ you only do the erase step in the koch curve (you know, each time you only erace the middle third), you get this:

size = 2*size*(1/3)^d

And therefore d = 0.631
(cool)

2. paulweerheim on said:

Thanks, really cool! Im 14﻿ and i love this

3. TheMrgreentoker420 on said:

2:33 thank you i﻿ would not have been able to concentrate if you didnt delete that little bit of pink left god damn my anxiety attacks

4. Lukasz Wiklendt on said:

Interesting that the Sierpinski triangle in 3D (using tetrahedrons instead of triangles) is 2 dimensional.﻿

5. OneFatMinute on said:

“to the one-th power” just means to the﻿ power of one. So “factor of three to the one-th power” means “factor of 3^1″ which is a factor of 3 (any number to the power of 1 is itself).

6. Jdonovanford on said:

What does “factor of﻿ three to the one-th power” mean?

7. DrJamesTanton on said:

Actually, a factor﻿ of a half won’t change matters. Area scales – no matter what specific formula it follows for a particular shape – by k^2 and that is all that is being used.

E.g. If the sides of a square are doubled, area changes by factor 4.
If the sides of a triangle are doubled, the area changes by a factor of 4.
If the radius of a circle is doubled, the area chanegs by a factor of 4.
If the sides of an irregular dodecagon are doubled, area changes by a factor of 4.

8. 1512dep on said:

with the triangles, wouldnt it affect the area because the area of a triangle if half x b x h so wouldnt﻿ the half change anything??

9. dudejohnny on said:

We have 3 dimensional﻿ photocopiers here… 