Firey Kapoera by kram1032

I'm not sure if I understand you here...
Symmetric formulae usually are easier to archeive and you can actually say, symmetry somewhat equals information reduction.

The sphere has an infinity of symmetries. It's the simples geometric Body, that is possible. All you need, is a point and a radius.
Any other 3D object is more complex than this.

By breaking the symmetry in some directions, you first get either rounded things that are just stretched a bit (ellipsoids and alike) or regular polyhedra.... (Cubes and such)

Breaking the symmetry even more, you get more and more complex objects.

The beauty from natural objets comes from their special symmetric properties:
Just as an example, I'll use a human body.

The most obvious symmetry we have, is bilateral, left and right. It's fairly but never totally perfect.

However, we have more symmetries, either more broken, or of a totally different kind.

Taking just a very (VERY) rough, short glance, you could argue, that we also are top-bottom billaterally symmetric. No sane human would say, this is definitely the case, but just imagine, you're an alien, who has a totally different body and is not familiar of the anatomies of this planet.
On the first glance, you might say, your legs are somehow symmetric to your arms. - However, they are twisted a lot.

More obvious again, is the symmetry of our hands and feet. It is still broken, but we sort of have five pretty similar fingers or toes on each hand or foot. The first of them is broken the most. - Here, you actually have some kind of radiary symmetry, with the center, where the hand connects to the arm. (Not that true for the foot... It's kinda stretched, additionally).
Also, if you hold your hand in graping pose and look from the right angle, you might notice, that they have an additional, somewhat mishapedly circular symmetry with four fingers sitting on top of a cricle and the fifth, the tumb, on the bottom of it.

Our heart sits off-center in our chest, but it itself is, slightly rotated to the body axes, quite symmetric. Our lungs are mostly symmetric, but caused by the heart, the left wing is a bit smaller.

Now to a totally different kind of symmetry, found everywhere in nature:
Fractal symmetry.
That's not quite directly a kind of symmetry. In fact, in terms of standard symmetries, you could have not a single one. But if you then look at the shapes, that repeat over and over again, forming often amazing patterns, there are often some kind of spirally symmetries to them and parts are somehow symmetric to other parts. That's probably the best way, to pack as much meaning into as little information as possible.

Repeating the same single process over and over again, creates incredibly complex shapes, that still look always the same and share some kind of odd symmetry, hard to actually be defined.

Fractal symmetry is basically, where parts of an object are symmetric to each other. It's a relative of selfsimilarity, in a way...

The point is, those formulas for bilateral symmetries are actually the simpler ones, usually.

yeah, this confuse me sometime too. But when you deal with a lot more algorithms n complex fractals, these are no longer a big deal.

no problem