|WikiProject Systems||(Rated Start-class, Mid-importance)|
I added the animated diagram.Cuddlyable3 16:05, 6 March 2007 (UTC)
10.22, 29 November, 2007
- I am sorry that I know no simple way to stop a browser from displaying the two animations. However you are free to hold a piece of paper over them. Alternatively you could view the text without illustrations in the edit window. Cuddlyable3 20:07, 2 December 2007 (UTC)
13 December, 2010
If you are using Firefox Mozilla (or similar), you can press the 'escape' key to stop the animations. It's probably the same in other browsers. —Preceding unsigned comment added by 126.96.36.199 (talk) 07:46, 14 December 2010 (UTC)
Isn't self-similarity related to symmetry somehow? Is there any literature that discusses the relationship between the two? They seem closely related. Although I could be totally off on this; call it a hunch. e.g. in regards to the Koch curve and the Mandelbrot set, the magnification that makes the sets interesting is just a scaling transformation right? And if some object retains some properties (hence similarity) under a transformation, thats the definition of symmetry. Just a laymen's understanding, so don't jump on me too much if I have something wrong here. If there is any discussion of this in the literature, it would be nice if it was mentioned here. Brentt (talk) 19:37, 10 June 2008 (UTC)
- This is the mathematical definition: Symmetry n. an attribute of a shape or relation; exact correspondence of form on opposite sides of a dividing line or plane. Cuddlyable3 (talk) 10:15, 26 November 2008 (UTC)
- Can anyone provide a clear example of a self similarity that only occurs under an anisotropic transformation? Cuddlyable3 (talk) 10:18, 26 November 2008 (UTC)
"Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole. For instance, a side of the Koch snowflake is both symmetrical and scale-invariant; it can be continually magnified 3x without changing shape."
That's not "any" magnification!
- It must be "discrete" (or "quantized") magnification, perhaps even integral.