Welcome to Fractal Forums

http://www.miqel.com/fractals_math_patterns/visual-math-iterative-fractals.html

Very cool sight.  Helps to make sense of it all; for someone like me who just stumbled into this.

Thanks for the reference. The crystal section is an eye opener. Its obvious now, but crystals in their natural forms are not faceted! Judging by his collection they are fractal! (http://www.miqel.com/crystals.html).

hmm - bit worried by #QW-01, the quartz scepter :o

Of course i have not put the observation as clearly as i meant to, but the large smooth faces are encrusted with smaller smooth faces etc as in a fractal, until the whole thing ends up looking like: well i will let you guess from the picture! :embarrass:
You know what they say  "....are a girls best friend!"

I wonder how much work has to go into some of these crystals to present them in this way, but i know the diamond industry enhances the rough diamond into its many facets.

Ok ya got muy attention again.. Something about my best friend?  I relooked at the sight & noticed how the crystals/minerals stones reminded me of my own collection & how I used to make jewelry out of them. Isn't all of nature fractal? Rough cut or faceted by man they are all beautiful. That being said I tend to wear "my best friends" more frequently!

Ha, that's my website!
Glad you like it ... i'm not a mathematician, but have been learning about and making fractals for almost 20 years.
There is a lot there which can be improved in that group of pages, so i'm very open to suggestions on making it a better introduction to fractals.
Also there are some images from here that are not properly attributed (msg me & i'll add a linkback if i've used anyone's pics)

Also i've found a paper i'd like to toss out there for the folks who truly understand the deeper math of all this ... i'm not qualified to evaluate it, but it's great reading & might contain some ideas for new equations or visualization techniques. I'm gonna move this to it's own thread

Chris King
March-Dec 2009
Mathematics Department, University of Auckland

"an investigation of the universality of the cardioid at the centre of the cyclone of chaotic discrete dynamics, the quadratic ‘heart’ forming the main body of the classic Mandelbrot set. Using techniques investigating and exploring the continuity, bifurcations and explosions in its related Julia sets, we demonstrate its universality across a wide spread of analytic functions of a complex variable, extending from the classical quadratic, through higher polynomials and rational functions, to transcendental functions and their compositions. The approach leads to some interesting and provocative results, including decoding dendritic island periodicities, and multiple critical point analysis, leading to layered Mandelbrot set 'parameter planes', and intriguing issues of critical point sensitivity in the irregular structures in the Mariana trenches of the more complex functions."

Hi miquel,

It is a cool site.

Reading the abstract reminded me of how difficult it is to put things mathematical in plain english.

First i would get rid of the mathematics and call ir science. And then i wou;d say aomething like science ha found out that the fractal form called the mandelbrot set helps us to describe physical phenomena like weather patterns and explosions and stuff. Take a look see  and play with the controls!

But i do not think the professor would get paid!

Where have you started this thread?

Hi Jehovajah,

Here's the thread you were asking about, but there wasn't much response (but one person wrote a good summary in layman's terms)
http://www.fractalforums.com/general-discussion-b77/long-academic-page-on-m-set-theory-maybe-some-new-ideas/