Talk:Self-similarity

message: Hyacinth 17:49, 1 October 2006 (UTC)
replies: text: 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)
thread_title:  Req diagram 

message: 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)
replies: text: 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)
thread_title: Symmetry

message: As self-affinity is a very strongly related but much less well-known concept, perhaps it should be merged here? JulesH (talk) 16:05, 26 September 2008 (UTC)
replies: text: 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)
replies: text: One example is the blancmange curve. There are other examples in the article on de Rham curves. Gandalf61 (talk) 11:30, 26 November 2008 (UTC)
thread_title:  Self-affinity 

message: "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.
:I also question whether the concept of "the whole" is applicable. What if, no matter how often you magnify or reduce the scale, you never arrive at an extremity? Unfree (talk) 21:02, 19 October 2009 (UTC)
thread_title: Any

message: I'm not an expert, but the phrase:
"If X\subset Y, we call X self-similar if it is the only non-empty subset of Y such that the equation above holds for \{ f_s : s\in S \} ."
cannot be correct.
First, what is  Y ?
Second, with this definition, all self-similar sets are countable. Indeed, if x in X, take all iterated images and pre-images of x via the functions \{ f_s : s\in S \} : this gives a countable set X' in X such that "the equation above holds". Since, by definition, X is the only subset such that the equation above holds, then X'=X.
Quantrillo (talk) 17:58, 2 March 2017 (UTC)
replies: text: For a non-expert, you sure seem to have a lot of expertise. A lot more than I have, anyway. If you have a reliable source showing how this section is wrong, please edit the article accordingly. CityOfSilver 17:59, 2 March 2017 (UTC)
replies: text:  Sorry for being not useful, but, even if I am a mathematician, I don't know what is the standard/most accepted definition of self-similar set and self-similarity. In fact, I came here because I wanted to use the expression "self-similarity" instead of "dilation", but it seems that dilations are not self-similarities and that, for instance, the real line is not a self-similar set (the non-surjectivity is crucial). So, either there is already an expert checking this page, or I can try to find one (outside Wikipedia, because I am not an expert of Wikipedia either).Quantrillo (talk) 18:14, 2 March 2017 (UTC)
thread_title:  Definition of self-similarity