Talk:Baker's map

message: The baker's map, as defined, has the entire square as an attractor, so the Hausdorff dimension is 2.  The action of the baker's map is to squeeze the left half into the lower half and the right half into the upper half after a flip. The horseshoe map has an attractor that is the product of two Cantor sets.  The map as defined in the horseshoe page has an attractor with fractal dimension –log(4) / log(a').  The minus sign is because a is smaller than 1 (as it needs to be smaller than 1/2).  So if a = 0.45, the fractal dimension of the attractor of the horseshoe would be approximately 1.736.    XaosBits 21:58, 1 Jun 2005 (UTC)
thread_title: Attractor

message: When the formula changed to "human readable format" I think it also changed into the horseshoe map, because of the -y.--MarSch 09:44, 23 Jun 2005 (UTC)
thread_title:  formula 

message: The russian version of this article has a nice image of a baker, which should be copied to wiki commons and then included here.  I tried to include the image directly from the russian site, but the inclusion did not work. 
The russian article also has a reatment of the symbolic dynamics which should be copied here. linas 19:15, 24 September 2006 (UTC)
thread_title:  Baker's map image 

message: I found this:
: 
:S_\mathrm{baker-folded}(x, y) = 
\begin{cases}
(2x, y/2)   & \mbox{for } 0 \le x < \frac{1}{2} \\  
(2-2x, 1-y/2) & \mbox{for } \frac{1}{2} \le x < 1 
\end{cases}
: 
I changed it to this:
: 
:S_\text{baker-folded}(x, y) = 
\begin{cases}
(2x, y/2)   & \text{for } 0 \le x < \frac{1}{2} \\  
(2-2x, 1-y/2) & \text{for } \frac{1}{2} \le x < 1 
\end{cases}
: 
The first uses \mathrm{baker-folded}; the second uses \text{baker-folded}.  When \mathrm is used, the hyphen becomes a minus sign; when \text is used, it remains a hyphen.  The first uses \mbox{for }; the second uses \text{for }.  In some contexts, those look much more different from each other than in the example above.  For example, contrast \min_\mbox{abcd} with \min_\text{abcd}:
: 
\begin{align}
\min_\mbox{abcd} \\[8pt]
\min_\text{abcd}
\end{align}
: 
The purpose of \mbox is to prevent line-breaks when TeX is used in the usual way as opposed to the way it's used within Wikipedia.  It shouldn't be used as a substitute for \text. Michael Hardy (talk) 15:56, 18 February 2010 (UTC)
thread_title:  \mathrm is not the same as \text (nor is \mbox) 

message: I removed this image because it didn't demonstrate the folded bakers map (or indeed the unfolded bakers map) as it was defined in the article. As evidence to this fact, note how the folded baker's map (as defined) would map a point arbitrarily close to (1, 1) to a point arbitrarily close to (0, 1/2) and the unfolded version would take such a point near to (1, 1), whereas this image mapped the top right corner (1, 1) to the top left (0, 1). Also note that both bakers maps preserve chirality (clock-wise gets mapped to clockwise) in regions they don't split whereas this map turned the right 5 into it's (squashed) mirror image. Can someone please upload a correct demonstration as it was a good illustration aside from the fact it was wrong. Nbrader (talk) 13:51, 18 April 2014 (UTC)
thread_title:  BakedBill.jpg