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Fractals, Mathematical Constants, and Binary Code

1984

ex-PiousWoo
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Anyone able to expound a little on mathematical constants such as Pi, fractals, Fibonacci Numbers, and Golden Ratios, etc.

By chance, I came across an article that the spirals in cone-shells conform to the Golden Mean. A quick glance into this area on the 'net covers everything from archiatecture, breeding rabbits, how trees grow, to the da Vinci code. So mathematics can be made to cover natural phenomena and woo-woo constructs, giving woo-woo people some sort of scientific footing. Isn't all this mathematics just a human way of attempting a reason for things. I'm sure binary code fits in here somewhere.

Any opinions keeping in mind those of us who are mathematically challenged most appreciated. Also, anyone recommend a CD-ROM that runs fractal images, or of global weather images from space?

ETA: url correction
 
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1984 said:
Anyone able to expound a little on mathematical constants such as Pi, fractals, Fibonacci Numbers, and Golden Ratios, etc.

By chance, I came across an article that the spirals in cone-shells conform to the Golden Mean. A quick glance into this area on the 'net covers everything from archiatecture, breeding rabbits, how trees grow, to the da Vinci code. So mathematics can be made to cover natural phenomena and woo-woo constructs, giving woo-woo people some sort of scientific footing. Isn't all this mathematics just a human way of attempting a reason for things. I'm sure binary code fits in here somewhere.
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Um, what was the question again?

Fractals are self-similar, the Fibonacci sequence is one of the simplest self-similar sequences if not the simplest one, the Fibonacci sequence converges to the golden mean, and self-similarity is kinda what you expect when bigger things grow on top of smaller things.
 
The Fibonacci sequence diverges, the ratio of 2 successive Fibonacci numbers converges to the Golden Ratio....
 
Oh, and: "Isn't all this mathematics just a human way of attempting a reason for things. I'm sure binary code fits in here somewhere."

Binary code fits in wherever any other math fits in. Binary code is just another way to represent numbers.

And, no, math is not a way to find a reason for things. Math is entirely abstract.

Hans
 
I've read that much of the Fibonacci connections are exaggerated. As for fractals, self similarity is a common method of producing them, but not all fractals are self similar. I'm not sure what you mean when you say the Fibonacci sequence is self similar. Do you mean it's recursive? And it's the ratio of successive terms, not the sequence, that converges to the golden mean.
 
I have a program called Fractals for Windows 3.1 and the whole thing is on a single floppy, remember those? Took overnight to render a 3-D Planet surface, very cool with mountains, lakes, and clouds on my old 486 but on the computer I am typing on right now it takes seconds. I'm almost positive someone would have something better by now, though. I still use it when I'm bored at work, not a bad run for a program I got about 15 years ago.
 
If you're interested in such things (and I know I am!) check out 'Innumeracy' and 'Beyond Innumeracy' by John Allen Paulos. I think that 'Innumeracy' covered the Da Vinci code thing... or was it another one... I'll check.
 
eri said:
If you're interested in such things (and I know I am!) check out 'Innumeracy' and 'Beyond Innumeracy' by John Allen Paulos. I think that 'Innumeracy' covered the Da Vinci code thing... or was it another one... I'll check.
Click to expand...

Another one of his books is 'Once Upon a Number'.

It's about applying mathematics, and mathematical reasoning, to stories and everyday life. Well, that's what the blurb says.

He talks about the Bible Code and other fun stuff.

Another great book is Ivars Peterson's 'The Jungles of Randomness: Mathematics at the Edge of Certainty'. Talks about and explains things like the 50-50 chance that two people in a room of 23 will share a birthday, and lots and lots of other wonderful stuff.

I have heaps of these types of books, sadly...
 
Try any of the fabulous (but few) books by Eli Maor. He covers a lot of the "simpler" questions that you're pondering here. He doesn't, that I know of, get into fractals and such, however.
 
epepke said:
Um, what was the question again?

Fractals are self-similar, the Fibonacci sequence is one of the simplest self-similar sequences if not the simplest one, the Fibonacci sequence converges to the golden mean, and self-similarity is kinda what you expect when bigger things grow on top of smaller things.
Click to expand...

Not really a question. Just a rambling :boggled: from someone trying to increase their understanding of mathematics, especially seeing as woo-woo people use it seemingly effectively. I'd like to be able to reason for myself, rather than say, "here's a Penn & Teller DVD, watch it, that's why I don't believe you".

What's "self-similar"?

Anyone know of a timeline chart with mathematical formulas, when and why each was conceived, by whom, and what was going on in the (scientific) world at that time. For instance, I know Pythagoras' Pi. But what was he looking for to come up with that. Einstein's E=MC2 is well documented. But who thought to come up with fractals, and why.

See what I mean here. These, to me, are incomprehensible fragments of mathematics. I will look into each suggestion given. Much appreciated. :o
 
1984 said:
Anyone know of a timeline chart with mathematical formulas, when and why each was conceived, by whom, and what was going on in the (scientific) world at that time. For instance, I know Pythagoras' Pi. But what was he looking for to come up with that. Einstein's E=MC2 is well documented. But who thought to come up with fractals, and why.
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You might want to start with http://en.wikipedia.org/wiki/Fractals That should get you started.
 
Starthinker said:
I have a program called Fractals for Windows 3.1 and the whole thing is on a single floppy, remember those? Took overnight to render a 3-D Planet surface, very cool with mountains, lakes, and clouds on my old 486 but on the computer I am typing on right now it takes seconds. I'm almost positive someone would have something better by now, though. I still use it when I'm bored at work, not a bad run for a program I got about 15 years ago.
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Lots of CGI software uses fractals. You might want to check out Terragen at http://www.planetside.co.uk/terragen/. :)
 
1984 said:
What's "self-similar"?
Click to expand...

It means that when you look at it at different magnifications, it's all prety much the same.

Take a Nautilus shell, which is one of those golden spiral thingies. If you magnify a small chamber, it looks pretty much the same as a large chamber.
 
1984 said:
But what was he looking for to come up with that. Einstein's E=MC2 is well documented. But who thought to come up with fractals, and why.
Click to expand...

That was fairly recent. Benoit Mandelbrot did it starting around the 1950s or 1960s. As for the why, it was to describe the geometry of some natural systems and of systems with positive feedback that do not settle down into equilibrium, such as turbulence.
 
epepke said:
That was fairly recent. Benoit Mandelbrot did it starting around the 1950s or 1960s. As for the why, it was to describe the geometry of some natural systems and of systems with positive feedback that do not settle down into equilibrium, such as turbulence.
Click to expand...
The Mandelbrot set is one of the more famous fractals, but there were others before it, such as the Cantor set (1884?) and the Koch snowflake (1904).
 
Thanks alot. Due to this thread I started my fractal generator this morning and it's now been 6 hours and I'm still playing with fractals. They seem to calm the mind which may lead to a little understanding in how the mind works.
 
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