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/sci/ - Science & Math

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6441044 No.6441044[DELETED]  [Reply] [Original]

Can someone here explain to me fractional dimensions? My Catastrophe professor mentioned it in passing and I'm trying to comprehend how that works.

>> No.6441078

It's a shape that makes up a fraction of a dimension, and can be scaled and repeated as a fractal. This explains it:

https://www.youtube.com/watch?v=js9nIgHA5FU

>> No.6441083

Only 3 dimensions exist. The rest of idealistic dimensions are just made up to explain quantum stuff, but they don't exist.

>> No.6441120

>>6441083
That's clearly not what OP is talking about.

There's a series of lectures called Godel Escher Bach. Just skip past the bits when Latiff is bullshitting his bullshit.

>> No.6441341

>catastrophe professor
I uhh... what?
Sounds like it would make a neat enemy or boss in a videogame.

>> No.6441391

>>6441044
so you say that an object has a fractional dimension (a fractal) this object is located in the embeding space (example we are in 3 dimensions) if you were to take your sobject at stretch it to an infinite size, it would only take up a fraction of the embedding space.

Example see the picture, if you were to make this infinitely big on a two dimensional plane, it would not fill up the whole plane. So we say it has a fractional dimension

Also Of you take the interval [0, 1] and remove the middle third, and then from each of the two remaining secions remove the middle third and continue this process infinitely many times, you would be left with just a scattering of points. NO think for a second, if a line (which we clearly dont have) has one dimension, and a single point and 0dimension, what is the dimension of a scattering of points?

>> No.6441392
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6441392

>>6441391
forgot to attach pic

>> No.6441559

>>6441391
that's absolutely wrong. It would take exactly 0 of the plane.


OP, fractional dimension is defined in term of scaling. Let N be the number of balls of the ambient space of radius L necessary to cover the space. Then, if as L goes to zero, N goes as some power of L, like N~L^d, then we say the set has dimension d.
You can see that for normal integer-dimension sets this yields the usual dimension.

>> No.6441562

>Catastrophe professor

Do you go to a super villain school? Where is it and how do I enrol?

>> No.6441580

>>6441559
sorry, that's L^(MINUS d)

>> No.6441628

>>6441559
this.

or to put it another way:

draw a line, zoom in 2x and now the line is 2 times as big, you can cut it to get 2 lines like the original one. thus a line has dimension ln(2)/ln(2) = 1

draw a square, zoom in 2x and now the square is 4 times as big, you can cut it to get 4 squares like the original one. thus a square has dimension ln(4)/ln(2) = 2

draw a cube, it divides into 8 similar cubes, so its ln(8)/ln(2) = 3 dimensional.

look at this pic >>6441392
if you zoom in 2x, you can get 3 triangles like the original one, so it has dimension ln(3)/ln(2), which is a fraction.

>> No.6443791

>>6441341
one of my friend's dads is a catastrophe engineer and he makes bank. i looked through some textbooks in his bedroom once - nothing was terribly confusing, mostly partial differential equations which could be decomposed easily.

>> No.6444627

>>6441341
>he hasn't even taken intro to quandary analysis