Fractal Geometry of Nature

[HydrogenBond]

I used to do digital artwork, although I don't do it as much anymore. One of the tools I liked was a set of filters called KTP or Kali's power tools. One of the filters in that version of KPT was frac-splorer. This filter allowed one to create an endless supply of fractal patterns. I would use these patterns as raw materials for further processing.

A technique that I developed was to take a similar series of a fractal pattern into Adobe Photoshop and blend them, flatten image. This kept the basic pattern but added more layers of variety such as spheres, fibers, etc.. I would then duplicate the resulting layer, flip one layer horizontally, blend the two layers, flatten image. Then duplicate the next resulting layer, flip one vertically, blend, flatten. The result was very interesting. What would almost always appear were little figures in the center of the symmetry, still surrounded by the basic fractal patterns in the perimeter. This technique suggested that certain mathematical manipulation of fractals patterns can lead to a different level of semi-fractal pattern in the center, that seem to set the parameters for the basic layout of nature's many critters. A loose analogy is the snail's shell is fractal. Inside is the snail.

[Turtle]

Originally Posted by HydrogenBond

I used to do digital artwork, although I don't do it as much anymore. One of the tools I liked was a set of filters called KTP or Kali's power tools. ...

You prompted a memory HB, and without regard to which side of my head it's recorded in, or you(all) record it in, here it is digitally.

Back when James Gleick's book Chaos came out, there was a ring-bound version that came with software. If I show a little less enthusiasm for doing fractal exploration these days, it's likely related to the untold hundreds of hours I spent with that software. Doing a quick web-search for any particulars, I find the software is available free online.

Chaos Downloads from Rudy Rucker's Wesbsite

[InfiniteNow]

Originally Posted by Turtle

I chanced on a PBS show last night entitled Colours of Infinity. Hosted by Arthur C. Clarke and featuring Mandelbrot himself, Steven Hawking, and Prof. Ian Stewart, it presented some breakthrough applications of fractals. Specifically, a new technique in image data compression that is phenominal! Basically, (as if!), any image is scanned or otherwise digitized and then a
a fractal equation is formulated on that image. Then taking that new fractal equation, it is applied to the zoomed in/pixelated view and the detail is 'filled' in!

Originally Posted by InfiniteNow

Sadly, my friend, it appears this was/is a local phenomenon. Upon reading your post, I was filled with a giddy excitement and launched your program schedule links. When I recognized they were specific to the pacific, of the northwest variety, I searched my local PBS schedule. But alas, it 'twas not to be. We have a wonderful Nature program on schedule, but my infinity will be colorless that day.

Originally Posted by Racoon

Did you remember to tape it Turtle-San??

There was no way I could stay awake until 4 in the morning for the re-airing of the first one I missed...

Originally Posted by Turtle

Alas , I saw Sunday, but the 4:00 am part didn't register. In other words, I was ready to go at 4:00 am MONDAY. Sorry I missed the mark.
I do have the homepage of Prof. Ian Stewart however and he has some cool fractal images as well as e-lectures on the subject. I think he's the one who developed the fractal compression scheme. Sorry again for my lameage.

Look what I found:

Fractals - The Colors Of Infinity (By Arthur...

[Pyrotex]

Damn! I wish I had time right now (at work!) to watch that video. But alas! Duty calls. Maybe later. At home. After I do my taxes. [sigh]

[InfiniteNow]

Originally Posted by Pyrotex

Damn! I wish I had time right now (at work!) to watch that video.

See, you're truly lucky then. It's always right now.

[Turtle]

Caught a show on fractals from NOVA tonight. It will be available to watch online soon: NOVA | Hunting the Hidden Dimension | PBS

Some highlights include that while Mandelbrot was castigated & mocked by his peers when he tried to have papers on his fractal geometry published in their journals, he persisted on his own and wrote the book this thread discuses. Many continue to castigate it as 'not math' etcetera, inspite of the universal applications it has demonstrated.

One such that I only learned about from the show is the fractal antenna, without which our cell phones would not function. Fractal antenna - Wikipedia, the free encyclopedia

Coming soon to a flickering box near you.

[InfiniteNow]

I saw it, too. Great program. From the history of the idea, to the events helping it form, to the applications of it... It talked of biology, and how even the rhythms of the heart can be modelled with fractal geometry.

Two thumbs up. Watch below:

NOVA | Hunting the Hidden Dimension | Watch the Program | PBS

[Thunderbird]

I caught the show last night terrific stuff! . The trees are fractal yea , but the pattern extends to the whole forest. What next ? The universe , quantum particles ?

[Guadalupe]

Originally Posted by Turtle

Caught a show on fractals from NOVA tonight. It will be available to watch online soon: NOVA | Hunting the Hidden Dimension | PBS

Some highlights include that while Mandelbrot was castigated & mocked by his peers when he tried to have papers on his fractal geometry published in their journals, he persisted on his own and wrote the book this thread discuses. Many continue to castigate it as 'not math' etcetera, inspite of the universal applications it has demonstrated.

One such that I only learned about from the show is the fractal antenna, without which our cell phones would not function. Fractal antenna - Wikipedia, the free encyclopedia

Coming soon to a flickering box near you.

Hi! Turtle

I enjoyed watching the program. Thanks.

[maddog]

I felt bad I missed that show last week. We had just moved and had left our
TV. At least we have one now. I will have to try and watch it off of pbs.org
website.

I have been fascinated by fractals for quite awhile now. First thing me and
some friends looked into was to see what other algebraic systems did with
this process. First looked at Quaternions (equivalent to Vector algebra in 3D).

Because Quaternions are an anticommunative algebra

i * i = -1
j * j = -1
k * k = -1

i * j = k
j * k = i

j * i = -k ... etc

you get strange pictures in projective 3D that are always twisted.

Somebody earlier in this post mentioned Julia Sets and they simply where
the constant C in equation z <- z^2 + C is the coordinate in the iteration.

The equation can be anything algebraic like

Z <- cos^2 (Z^2) + C

and you will get an a fractal that will look like and earthworm about the
x axis.

And so on.

maddog