Fn=Fn-1+Fn-2

F0=0, F1=1

Yield:



Further:

Somebody correct me if I'm wrong here.

The way I understand it is that many fractals are the graphs of equations meant to produce random results. Yet these seemingly random patterns, when graphed, make distinct and beautiful geometric shapes, some of which occur in nature. We've seen examples of that in the pictures in this thread. Thus part of the lesson seems to be that there is actually a pattern to randomness. Is that a fair thing to say?

So let me take it a step further. As a frequent card player who has to deal with supposed randomness on a regular basis, could we then extrapolate from this idea that even randomness has a pattern, and give credence to the idea that luck comes in streaks? Give it a mathematical explanation as it were?

What say you math geeks?

Fractals aren't "random" per se - They are based on a simple, but powerful, equation that generates escalating (repeated) patterns based on a seed input...

They may seem random, inasmuch as oil swirling in water seems random, but they are highly structured and reflect a nested series of ever-repeating consistencies.

And as a card player and engineer who's taken statistics, I can tell you that with sample sizes large enough, you can see all kinds of interesting outputs. Luck runs in streaks, sometimes. Flip a coin 15,000,000,000 times and you'll end up having some instances of heads coming up 27 times in a row. Are some people luckier than others? Well, yes, actually. While most people will have average luck or near to it, some outliers, just because of sheer numbers, will have great or terrible luck. It's not anything inherent in the person, it's just statistics.

Ham

_________________
Do you believe yet?

So if one were to try to create an equation that would generate "random" results (if that's even possible), and this formula was graphed, would it look anything like a fractal? Or am I just totally misguided in my belief that there is no true randomness?

I believe that the concept of "randomness" can be applied to any phenomenon in which the available data-set defies or overwhelms one's tools, or abilities, to analyze it - And apply a modicum of "predictability" to its' outcome.

"Chaos Theory" is a misnomer - The minute you can put a finger on it, you can start making sense of all the "noise"; and patterns begin to emerge.

True randomness cannot exist in this universe. It would imply that there are some things that don't have rules governing their behavior; things that don't follow the rules of reality/existence/physics. It would imply, on a greater level, that something can come into being, or cease to exist, without reason or purpose.

That we may not understand certain things, just yet, doesn't mean that they will never be understandable. Hence, our views of randomness or chaos, as a category of existence which remains, as yet, inscrutible.

True "randomness" defies the primary principle of causality. And that's an impossibility.