07 April, 2011

A-Z Blogging Challenge: F Stands For: Fractals


A fractal is "an object or quantity that displays self-similarity". Some characteristics of a fractal are:

1. It has a fine structure at any small scale.
2. It cannot be easily described in traditional Euclidean geometry.
3. It is self-similar.
(Exactly or approximately equal to part of itself.)
4. Its Hausdorff dimension is greater than its topological dimension.
(The Hausdorff dimension being an extended non-negative real number associated with metric space. And yes, I get a bit befuddled there, too.)
5. It has a simple and recursive definition.
(A recursive definition is used to define an object in terms of itself.)


One real-world example of a fractal, besides the usual repeating shape, is that if you measure a coastline with a ruler the longer it comes out in the measurements the shorter you make your ruler. This is because inlets, bays, large rocks, and other such formations will become factors the finer you get. (The coastline paradox.)


But though the math and concept is quite interesting, fractals are visually amazing. They're so intricate, repeating over and over again in triangles, curves, spikes, branches, and so many other patterns. They show up in nature, and also have modern applications in things like computer graphics.



*****

I believe it's already been established that I'm a fan of NOVA and PBS science shows, but another video won't hurt, will it?

Hunting the Hidden Dimension NOVA Program

If you want to have some fun with fractals:

http://www.coolmath.com/fractals/fractalgenerators/generator1/index.html
http://www.chaospro.de/ (Free software)
http://www.fractalposter.com/fractal_generator.php

Sources:
http://mathworld.wolfram.com/Fractal.html
http://en.wikipedia.org/wiki/Fractal
http://en.wikipedia.org/wiki/Fractal_dimension
http://en.wikipedia.org/wiki/Hausdorff_dimension
http://en.wikipedia.org/wiki/Self-similarity
http://en.wikipedia.org/wiki/Recursive_definition
http://mathworld.wolfram.com/CoastlineParadox.html

*****

What do you think of fractals?


-----The Golden Eagle
Enhanced by Zemanta

48 comments:

Tere Kirkland said...

This kind of reminds me of how I write. The longer I'm immersed in the world with the characters, the shorter my "ruler" gets. The more tiny details I add to the story.

Thanks for the awesome visuals!

Heather said...

This is way too cool! I love this! I didn't know much about fractals. Thank you for informing us!

Siv Maria said...

Thanks for the interesting information as usual. Love Fractal art.

AllMyPosts said...

I don't even know what Fractals are !!!!

Thanks for sharing!! The pictures are all cool!!!

with warm regards
http://becomingprince.blogspot.com

Gary Baker said...

As a programmer I was playing with fractals and the Mandelbrot set many years ago. New computers let us see 3D fractals in mind blowing forms. Fascinating. I might dig out my old programs and have a play. Cheers.

Old Kitty said...

Although the maths and physics side of these amazing things are over my head - I do think they are beautiful to look at!!!

I can't view the video link cos I'm at work but will do when I get home!

Great F post!! Take care
x

Kristin said...

Very cool looking

Kris Kaumeyer said...

They're so trippy to look at. I fell like sinking into dark, endless void when I stare at animated fractals. It's the stuff dreams are made of.

M.J. Fifield said...

Hey, my significant other just wrote an android ap that has something to do with fractals. He tried to explain it to me but I didn't get it.

I think fractals are kind of pretty though.

Michael Offutt said...

Fractals are really cool. I downloaded an app for the iPad that created them. However, it really taxes the poor iPad's limited processor. I don't recommend the app because of this.

Alex J. Cavanaugh said...

I guess a Kalediscope could be considered a fractal. Or at least some of the resulting images.

Cherie Reich said...

Great post! I loved the images you used for fractals.

jabblog said...

They are indeed beautiful and intriguing. You should look at Tumblewords' blog at http://firsttumblewords.blogspot.com/- she produces many wonderful fractals.

Deborah Walker said...

That's fascinating. I love the phrases 'self-similar' and 'recursive definition' very evocative, there could be a story in there.

the writing pad said...

I've always shied away from finding out about Fractals because of the complexity of the subject - but I think I do now begin to see a glimmer of light (as well as some lovely images)
Thank you!
All best
karla

Lauracea said...

Spare a thought for a math simpleton here. Mind you, I'm learning on this blog. Are you going to test us at the end? :)

Tiger85 said...

Very interesting stuff. Thanks for sharing this. The images are beautiful too. =)

http://tigeronmybookshelf.blogspot.com/

Theresa Milstein said...

Love the fractal pictures.

I'm glad everyone isn't just dong writing-related A to Z posts.

Carole Anne Carr said...

That post is utterly amazing. I am fascinated by anything like this, especially the structure of atoms.

TheyCallMeVarmit said...

Was unaware of what fractals were. But, not anymore! nice post!

Matthew Vanacore said...

Great post! Fractals are indeed, fascinating. The pictures are all wonderful and your descriptions are on the ball.

Margaret Hall said...

Interesting, vibrant posting~!! Loved the fractals that you shared, they are beautiful...Thanks for an interesting "F" posting...

See you for "G"...

http://timeforabucketlist.blogspot.com/
http://imagesinthought.blogspot.com/
http://the-old-story-tree.blogspot.com/
http://bagladythoughts.blogspot.com/

nutschell said...

My goodness; What mesmerizing pictures! The colors just pop out at you. I'm not exactly math-inclined, but these fractals are really interesting. thanks for sharing!
nutschell
www.thewritingnut.com

Michelle Merrill said...

Those images are awesome! I have to admit, I was lost through most of the fractals definition but if fractals create images like those, I like them already :)

Josh Hoyt said...

This is so cool i love your blog and the cool science. Thanks for the new information.

Shannon O'Donnell said...

Wow. I would never have thought of that! :-)

Lynda R Young said...

I LOVE fractals. They are so artistic and appealing to the eye.

Anne K. Albert said...

Stunning pics. Thank you. :-)

li said...

Gorgeous pics. I almost bypassed this post because I thought it said "fractions", and math makes me run and hide under the bed.

Brian said...

Those were all so cool and you did a great job putting them together for us. We love science shows here too!

Jack Edwards Poetry said...

Really interesting post. Thank you.

Liz P said...

I love fractals! Great post!

Michael Di Gesu said...

FA-BU-LOUS! These images are awesome!

Thanks for sharing fractals with us.

Emily Rose said...

Whoa, those are beautiful!

Trisha said...

Fractals are so pretty! :D

Sheila said...

I find these very fascinating! You are giving me some fun things to show my kids at school. I am not sure that I could explain about them as you do, but it would be interesting to see what they have to say.

Sheila Staley : Reviewer & Writer
Book reviews and Author Interviews at my blog at http://whynotbecauseisaidso.blogspot.com/

laughingwolf said...

pretty neat, ge... we studied em in my computer animation courses :)

i.ikeda said...

Love it! Fractals not only look amazing, but their properties can serve as the basis for wonderful metaphors. Great post.

Thank you for the follow.

Tomara Armstrong said...

You definitely get me thinking every time I visit your blog... blows my mind.
~2

Duncan D. Horne said...

Still not quite getting to grips with fractals, sounds very complicated!

Duncan In Kuantan

Talli Roland said...

I've never heard of fractals before. Interesting!

Madeleine said...

Wow nice images. I never heard that term before. :O)

Charles Gramlich said...

These are just plain cool.

doreen said...

You are brilliant. I had no clue what a fractal was. I am loving this A-Z challenge; I really had not expected to learn so much.
Hats off to your folks for being fabulous teachers.

The Golden Eagle said...

Tere: I do the same thing. :)

You're very welcome!

Heather: Anytime. :D

Siv: You're welcome.

It's so cool to look at.

Abhishek: You're welcome! Glad you liked the pics. :)

Gary: 2D is amazing enough!

Old Kitty: I think so, too. :)

Thank you!

Kristin: Aren't they? :)

Kris: They are--endless shapes and colors like that are so not-found-in-nature the only place for them seems to be in dreams.

M.J.: He wrote an Android app for fractals? Wow.

Me, too. :D

Michael: I read a review of a fractal program that mentioned it crashed the reviewer's computer--I wonder why it takes so much processing power.

Alex: True! I love looking at through those things. :)

Cherie: Thank you!

Glad you liked them!

Jabblog: I will definitely have to check that out! Thanks for the URL.

Deborah: They are interesting phrases, aren't they?

The Golden Eagle said...

Karla: You're so welcome! :)

Lauracea: I hope I didn't bombard you with too much math there--I thought some readers might find that part interesting.

Nope . . . although, you're not the first person to mention it and it's giving me ideas. ;D

Tiger85: You're welcome!

Theresa: I'm glad you enjoyed the pictures!

I suspected a lot of people would be doing writing posts, and since I love science (AKA total nerd here) I decided to write these. :)

Carole: Atomic structure is definitely interesting! The way the electrons create bonds and the protons, electrons, etc.

Varmit: Well, I hope you find knowing about fractals useful sometime in the future. :)

Thank you!

Matthew: Thanks!

And thank you for following my blog as well. :)

Margaret: You're welcome! I'm glad you liked the post.

Nutschell: The colors do jump--they're so striking.

You're welcome!

Michelle: I'm glad you liked the pics I posted! :)

Josh: Aww, thank you!

Anytime!

Shannon: For the post, or the fractals themselves?

Lynda: They are!

Anne: You're welcome! :)

Thanks for coming by and commenting.

The Golden Eagle said...

Li: Glad you liked the pics!

I'm kinda of a math geek . . . I love learning about numbers. :)

Brian: Thank you!

Science shows are the best. :)

Jack: Thanks! You're quite welcome for it.

Liz: Thank you!

Michael: Thanks!

You're welcome. :)

Emily: Fractals can create all kinds of amazing images. :D

Trisha: Definitely!

Sheila: I hope your kids have fun with fractals! :) You might want to try www.coolmath.com--they have some, well, cool stuff there.

Laughingwolf: Wow. It must have been interesting to learn about them!

i.ikeda: Good point!

You're welcome! :)

Tomara: I hope you enjoy visiting--even if I end up, er, blowing your mind. :P

Duncan: The math is rather complicated--I don't get much of it, either!

The Golden Eagle said...

Talli: Glad you thought so!

Madeleine: I'm glad you liked the images!

Charles: They are! :)

Doreen: All of the factual stuff is from Wolfram and Wikipedia--two amazing sites! The people who write those articles much be amazing.

I hadn't either! So many A-Z posts are so interesting and informative.

Thank you!