First of all, I would like to tell you that if you are busy or are not interested in the discussion, you can dismiss it as you like. I wanted to discuss it with you because I think maybe you are knowledgeable and also because I'm having a holiday now.
I know about Sierpinski's Triangle, the no. of triangles increase in a sequence of 3^r and the hollow part of triangles Ur+3^r, and the length ½^r. If we write out the value of Ur+3^r, we get 0, 1, 4, 13, 40,121…, find each difference, 1, 3, 9, 27, 81…, and find the multiple, we get 3, 3, 3, 3, 3… Differentiate 3^r we get 3^xln3 and we found the gradient......
Of course there is also Sierpinski Pascal triangle.
All these ideas are related to ‘change', and indeed the ideas of change are everywhere, from economics to chaos, from evolution to calculus, from thermodynamics to relativity, from quantum mechanics to probability, and most importantly, they are very interesting.
‘Static' ideas or ‘methodical' ideas are of course in my opinion boring. But it should not be mistaken as ‘universal' ideas which are not time-based, and is about general principle or concept but may or may not be a theory and may changes through a change of perspective like from Newtonian physics to Einstein physics.
Figuratively, static are like ‘facts', methodical are like ‘logistics', time-based like ‘history', universal like ‘unification', example are the string theory which “claims” to unify all fundamental energy in one single “theory”. But I think it is a concept than a Theory, or rather it can only be ‘thought' of as a concept because as far as it is conceivable, we cannot prove such concept, but a little imagination can kind of “prove” to us that it is “real”.
Of course, we may think, what ARE real and what ARE proofs, again it has to go through so many layers of ‘subjective' and ‘objective' factors, or is it just like different ways of looking at the same thing, or is it a paradox, or like the imaginary number -1^1/2 where it gives two answers at the same time? When you said ‘related' I got excited by it, could it be analogical-based, or unification like the molecule of sodium chloride or any other molecules….. Ok, I'll stop my nonsense for now.
So what relation is there about chaos and Sierpinski's Triangle?