Haven't heard any of those before... How do they operate?
Sacred geometry and hyperdimensional physics are difficult to summarize, and unfortunately I can't link to any webpage that is devoid of new age jibberish. I guess David Wilcock's
Divine Comsos would be a good place to start though.
It's the third book (with the best start) of his Convergence series:
Shift of the Ages
The Science of Oneness
Divine Cosmos
I feel particularly interested in the platonic solids. Do you have references?
If you want to see lots of pictures, nose around here:
http://www.goldenmean.info/
EDIT: Watch this video, it's actually quite good:
The purpose of DNA.
Do you mean destinies comes directly from laws and then there is now choice or possibility beyond them?
"Law" is actually a tricky word here. Again, I simply mean the way energy flows, which is always governed by certain laws of nature, such as gravity or the push and pull of air pressure, intellectual concepts, physical attraction etc. Nothing escapes the strongest natural force active in a certain time and space.
So, yes, our destinies come directly from the laws of nature, on all levels. Without those laws, our feet wouldn't stick to the surface of this planet, there wouldn't be blood pumping through our bodies, there would be no plants to nourish us, indeed life as we know it wouldn't be possible. The universe wanted it like this, indeed, there was only one way for the universe to be, and that is how it is right now, with you conditioned to be you and me conditioned to be me for a couple of years. If there ever was a Big Bang, your current life was a natural consequence of all the events that would follow as a result of that bang. In other words, your life was implied from the very beginning of creation. You were meant to be, just like I was meant to be and even tyrants and criminals were meant to be. So why bother going beyond anything? Why bother trying to transcend your fate, or the inevitable unfoldment of events in time? You are fate. You are time.
I'll repeat the process. To what extend to we produce, in the sociality and in the matrix, our own nature?
You don't produce your own nature, you are your own nature, at any given point in time. From that nature certain fruits arise.
To what extend is the nature of "those ones" determined by their developing surroundings?
They come into the world with the full potential of their mission, but the way they develop is determined by their surroundings. The two go together, there's no causal connection. From a psychological or pedagogical point of view one might say there is a causal connection, but the astrological perspective turns that picture upside down because the type of parents and schooling one will receive is already visible when one is born. It's better to not dwell too much on causal relationships.
I don't think we have a definite nature
Part of us is subject to change, other parts are not. You can change and add certain software, but you can't replace the operating system. Crude example, but it's a useful metaphor.
I think we are culturally and materially produced on top of biological platform that although defines limits, those limits operate in complex multidimensional ways.
True, but those complex multidimensional ways are still occuring in mathematically predictable ways.
what's a wave of creation?
Like a wave in the ocean. It's visible for a short while and then it disappears again.
does nature imply purpose?
I'm not sure. Purpose for what or whom? So far I've only come to terms with the fact that nature is predictable. I don't think one can logically deduce purpose from that. But again, I'm not sure.