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Is there a difference between a fractal dimension, and "human
imperfection" when creating jewelry? What distinguishes the
acceptable fractal dimensions from other imperfections of a man
made object; or is imperfection just a poorly executed fractal
dimension?
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Fractal is an object made of self-similar, but smaller objects.

Take a broccoli. Broccoli is fractal. We can take a bunch of

broccoli and start taking it apart. We quickly notice that all parts

regarding of size look alike. Not the same but similar. That is

necessary characteristic for fractal.

Is there an ugly broccoli ? No. Is there beautiful broccoli ? No.

Broccoli is simply interesting. One can study it’s shape for hours

and will keep finding variations. Nothing is the same, but similar,

and every element will have the same fractal dimension.

What is fractal dimension? Staying away from mathematics, draw a

square on the paper. We can easily compute the area and the perimeter

of this square.

Replace each side of the square with two lines joined at some angle

facing inwards.

What just happen is that area of the square become smaller, but the

perimeter became larger. We can continue this process forever and if

we do, we observe that length of the perimeter is infinite, but the

area is not. Area would become smaller and smaller tending to some

finite quantity. This is actually quite remarkable.

We have perimeter of infinite length encompassing finite area.

Going back to broccoli, is it possible to exactly measure the

surface of the broccoli ? Absolutely not, but we can measure the mass

and there by the volume by simply weighing it.

What about jewellery? Every article of jewellery has certain feel

about. Some call it soul, which is fine. Formally it is perception of

it’s fractal dimension. As long as “imperfections” have the same

fractal dimension, they will look like they belong.

To understan this study the work of Auguste Rodin. His surfaces

always rough and unfinished, but they belong. Take technique like

pave. If we examine cut by cut; stone by stone, - there is nothing

perfect about it. Nevertheless, some pave looks like it contribute to

the article of jewellery, and some looks like it been glued on top of

article by mistake. This is what is called “setter’s talent”, or we

can call it fractal intuition.

One more example. How does an artist make hair look like it has

life.

It is not possible to draw every single hair. What about sculptor

who works in marble ? Try to convey this feeling of wind playing with

hair in CAD.

Good luck if you decide to try. Nevertheless, it is accomplished by

thousands of artists on daily basis. A few strokes of pencil, or few

cuts with chisel and it is done.

On some level artistic talent is an ability to recognize and

reproduce fractal dimension of and object. That is why caricature

works. Caricature and it’s object do not look alike, but they have

the same fractal dimension.

Leonid Surpin

Studioarete.com