It’s only a constant because we’re making a repeating 2-d object behave like three-d. I’ve written on this before.
Anyway… this is one of the reasons why we can’t calculate Mersenne’s Primes, people don’t grasp that polynomals- which fractals have to behave the rules of progressive series of- from the highest to the lowest (literally in that order)- WITHIN, are a series parallel to our number theory. If you start big, and work down… these things don’t go on for infinity, they break down into angles relative to their square root, in relationship to the shape squared above it. You can find all the primes patterened off of that. All fractals behave to these rules that are based on polynomal successive series. It’s remarkably simple- retardedly simple, and early mathematics in the west were built on this very assumption, but the stoics and aristelians butchered this system of numerics early on. And we’ve suffered for it ever sense. In our current system, we’re aware that spirals dominate these series, but don’t officially know why. We also know that the patterns seem to be finite, but when applied geometrically, goes on forever… but no one quite explained why other than numbers such as 1 2 3 4 5 go on forever.
At bottom, I’ve found it to be a simple cognitive glitch. Classical systems of Abacus using different base numbers, such as Chinese versions, are better at navigating fractal distributions via multiple root systems.
We need to note the obvious about these… it’s the formulas we have that are failing us… they ‘appear’ to go on forever, but don’t actually go on forever. It’s because they simulate depth… but the formulas lack expressions of depth in and of themselves. Hence the need for polar and grid mapping of position when you focus in on any given point. That picture above you present doesn’t go on forever… 0.5 picoliters is the max for the average high end computer you would expect to find in a math institute… then it becomes meaningless. The formula is devlivered visual, and it stops at that size. It tells us more about how our brain processes information, than how infinity works. We didn’t evolve to comprehend visual infinities, just to accept things go on for a very long ass time, and that such journeys are likely not worth the energy expended. What is important about such fractals is the way prime numbers play out in them. Fractals give us the advantage that most series play by polynomal rules, outside of rules of progressive succession. You can get all sort of weird bifurications resulting. rDNA seems to encode on this basis, as many plants and cellular organizations play by this rule. Life doesn’t stretch out for infinity… there isn’t a cell the size of a planet that kept growing forever… like fractals, size and logistics limits it’s rules… something a limited mathematical model doesn’t compensate for. However… for the size and chemistry of life on earth… these bootleg eternal objects are dead on in terms of importance. They might not be eternal, but they are the building blocks that ceelular intelligence builds larger lifeforms out of. Hence the importants, and my focus. It goes well beyond mathematical curiosity, it’s a fundamental question of philosophy. Just no good to get stuck in the cognitive glitch of assuming they go on forever when… well, they never do. Just we such at math so bad we don’t have a native way in our mathematics to close open ended math problems realistically.
That cognitive glitch is mystical though admittedly, from a biological perspective. Just doesn’t give you the full picture. But the best mathematicians historical have also been mystics, working with the paradoxes of the systems they are presented with. We gotta remember the mystical, cultic roots of mathematics, from egyptian and babylonian temples to Pythagorians and Perganum Stoics. So… it’s not unhealthy to assume this has religious roots. Religion always has had this element… just some fairly secular people can also think it once it’s formalized without the need for further mysticism. They are call scientists, and they tend to be remarkably stagnant and uninventive. And their always amazed that religious people can be good scientists too. Absolutely blows their mind… but takes massive ignorance on their part to not look into the origins of how the systems they used came into existence.
Hence, kudos to this thread- your carrying on a beautiful and most ancient tradition. Just don’t annoy me by saying the son of god talks through the fractals to you. Just appreciate God exists, and he knows why your interpreting such things so wrongly, and loves you for seeing beauty in such misunderstandings. Means at the very least your exploring your own potentiality and nature through them, which is quite worthy.
