Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
General Math
Calculus
Differential Equations
Topology and Analysis
Linear and Abstract Algebra
Differential Geometry
Set Theory, Logic, Probability, Statistics
MATLAB, Maple, Mathematica, LaTeX
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
General Math
Calculus
Differential Equations
Topology and Analysis
Linear and Abstract Algebra
Differential Geometry
Set Theory, Logic, Probability, Statistics
MATLAB, Maple, Mathematica, LaTeX
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Mathematics
General Math
Fractal Dimension & Degree of Freedom
Reply to thread
Message
[QUOTE="Mark44, post: 6087274, member: 147785"] Normally "degrees of freedom" are integral values, but in non-standard regression (which is something new to me), non-integer values are permitted. I haven't read of the term "degrees of freedom" used in discussions of fractals, though, but I haven't done any recent reading about fractals, so maybe someone has made the connection. The usual meaning of the term fractal is that a curve or surface is self-similar, meaning that it looks the same even when magnified over and over. The usual method of measuring curves assumes that for small enough intervals, the curve is approximately a straight line segment, so we can add up all the pieces to get the overall length of the curve. On the other hand a curve such as the Koch snowflake has little jaggies at all resolutions, so no matter how much we magnify the image, we can find any straight line segments. Mathematically, this curve is nowhere differentiable. Although the area of the Koch snowflake is 1.6 times as large as the triangle it is based on, the perimeter of the Koch snowflake grows large without bound (see [URL]https://en.wikipedia.org/wiki/Koch_snowflake[/URL]). Normal geometric curves have a defined perimeter, so because the perimeter of this figure becomes infinite, but encompasses a finite area, it is considered to have a dimension somewhere between 1 and 2 (about 1.26 according to the wiki article). [/QUOTE]
Insert quotes…
Post reply
Forums
Mathematics
General Math
Fractal Dimension & Degree of Freedom
Back
Top