Logo by Maya - Contribute your own Logo!

END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval,
thanks and see you perhaps in 10 years again

this forum will stay online for reference
News: Support us via Flattr FLATTR Link
 
Home Help Search Gallery Downloads Login Register
*
Welcome, Guest. Please login or register. October 14, 2024, 09:35:34 AM


Login with username, password and session length


The All New FractalForums is now in Public Beta Testing! Visit FractalForums.org and check it out!


Welcome to Fractal Forums > Fractal Art > Fractal Art Review > MC Escher's "Circle Limit" pictures
Pages: 1 [2]   Go Down
« previous next »
  Print  
Share this topic on DiggShare this topic on FacebookShare this topic on GoogleShare this topic on RedditShare this topic on StumbleUponShare this topic on Twitter
Author Topic: MC Escher's "Circle Limit" pictures  (Read 9639 times)
0 Members and 1 Guest are viewing this topic.
Max Sinister
Conqueror
*******
Posts: 114
« Reply #15 on: May 28, 2016, 12:17:57 AM »
That's also true. Well, even the experts haven't agreed on how to define fractals.
Logged
fractals + procgen: My shapeways shop
Max Sinister
Conqueror
*******
Posts: 114
« Reply #16 on: June 08, 2016, 11:20:36 PM »
Quote from: Chillheimer on May 27, 2016, 09:18:09 AM
But I'm wondering about what kind of dimensions are we talking about? if it's the fractal dimension as in Hausdorff Dimension, lots of fractals have an integer dimension, like the mandelbrot set with 2.

Just checked the German WP article again and found something we missed:

Mandelbrot himself defined fractals like this: A fractal is a set which Hausdorff dimension is bigger than its Lebesgue covering dimension.
(German: "Ein Fraktal ist eine Menge, deren Hausdorff-Dimension größer ist als ihre Lebesgue’sche Überdeckungsdimension.")

Cantor dust has L(ebesque) 0, but H(ausdorff) 0.6309...

A Hilbert curve has L=1, but H=2.


This allows fractals with a dimension that's exactly 2.
Logged
fractals + procgen: My shapeways shop
Pages: 1 [2]   Go Down
« previous next »
  Print  
« previous next »
 
Jump to:  

Related Topics
Subject Started by Replies Views Last post
"Dual-power" formula pictures Theory FrozenOwl 0 3768 Last post October 04, 2010, 10:18:32 PM
by FrozenOwl
I had a vague idea that "fractal" was related to "pretty pictures" Meet & Greet Repomancer 5 9567 Last post October 10, 2012, 02:04:23 AM
by David Makin
Mandelbrot "Adaptive" Escape Limit? Programming nessalc 3 3811 Last post September 21, 2013, 04:46:48 PM
by DustyMonkey
Are all "particles/quarks/universe" fractals of "Extended Periodic Table(s)"? (new) Theories & Research sunshaker 4 2894 Last post January 15, 2016, 10:28:02 PM
by M Benesi
Fractal like "Escher Julia" made by glue Fractals Applied or in Nature hgjf2 0 3408 Last post May 19, 2017, 09:22:14 PM
by hgjf2

Powered by MySQL Powered by PHP Powered by SMF 1.1.21 | SMF © 2015, Simple Machines

Valid XHTML 1.0! Valid CSS! Dilber MC Theme by HarzeM
Page created in 0.136 seconds with 24 queries. (Pretty URLs adds 0.007s, 2q)