Originally Posted by **Georgeo57** How does moving inwards from an atom not satisfy my proposition? We're exploring progressive smallness, and moving inwards seems indispensable to doing this.
It might help if you posted your definition of fractal, and directly related it to the proposition. |

'Moving inwards' is phrase fraught with the difficulties of imprecision.

Moving inwards from one atom in the way you describe implies moving outwards from any other atom.

And if you pick something 'inside the atom' and move inwards again you are therefore moving away from the rest of the structure of that atom.

Is this what you really meant?

I think you mean something like this:-

When I was younger there was a brand of liquid coffee essence that came in a bottle, rather than the dried granules we have today.

The picture on the bottle showed a waiter serving someone the coffee.

The waiter had one of those waiter trays he held up in one hand.

On that tray was a bottle of the coffee, with the picture just discernable.

I used to think of the possibility of the infinite regression of ever smaller pictures of waiters holding trays with a bottle with a picture of a waiter holding a tray..................

This property is called self similarity and is a property of fractals.

This means that at ever decreasing scales each 'picture' is the same but contains smaller and smaller versions of itself.

So perhaps you can now see that this was a serious suggestion to help you take your proposal forwards.

To properly define fractals you need to first know the meaning of two mathematical terms

Metric

Dimension.

I say mathematical because the mathematical definitions are wider than those used in Physics, and this extra width is needed.

A metric is a real valued function, d, defined on a non empty point set X (finite or infinite) with elements {x, y, z.....} that satisfies the metric axioms which are

For every pair of elements of X

(1) d(x,y) >= 0 and d=0 implies x = y

(2) d(xy) = d(y,x)

(3) d(x,y) <= d(x,z) + d(z,y)