Difference between revisions of "File:Frac1zt.jpg"
(Iterates of function $T(z)=-1/z$ $y=T^n(x)$ is plotted versus $x$ for various real values of number $n$ of iteration. The non-integer iterates of function $T$ are evaluated using the superfunction $\displaystyle F(z)=\tan\left(\frac{2}{\pi} z\r...) |
(→C++ generator oc curves) |
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Line 11: | Line 11: | ||
$\displaystyle G(z)=F^{-1}(z)=\frac{2}{\pi} \arctan\left( z\right)$ |
$\displaystyle G(z)=F^{-1}(z)=\frac{2}{\pi} \arctan\left( z\right)$ |
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− | ==[[C++]] generator |
+ | ==[[C++]] generator of curves== |
+ | |||
+ | File [[ado.cin]] should be loaded to the working directory in order to compile the [[C++]] code below. |
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+ | <poem><nowiki> |
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+ | #include<math.h> |
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+ | #include<stdio.h> |
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+ | #include<stdlib.h> |
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+ | #define DO(x,y) for(x=0;x<y;x++) |
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+ | #define DB double |
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+ | |||
+ | #include"ado.cin" |
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+ | |||
+ | DB F(DB n,DB x){return tan( (M_PI/2)*n+ atan(x));} |
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+ | |||
+ | main(){ FILE *o; int m,n,k; DB x,y,t; |
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+ | o=fopen("frac1z.eps","w"); |
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+ | ado(o,1002,1002); |
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+ | #define M(x,y) fprintf(o,"%7.4f %7.4f M\n",0.+x,0.+y); |
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+ | #define L(x,y) fprintf(o,"%7.4f %7.4f L\n",0.+x,0.+y); |
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+ | fprintf(o,"501 501 translate 100 100 scale 2 setlinecap\n"); |
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+ | for(n=-5;n<6;n++) { M(-5,n)L(5,n)} |
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+ | for(m=-5;m<6;m++) { M(m,-5)L(m,5)} |
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+ | fprintf(o,".005 W S\n"); |
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+ | M(-5,0)L(5,0) |
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+ | M(0,-5)L(0,5) |
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+ | fprintf(o,".02 W S\n"); |
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+ | n=0;DO(m,1001){x=-5.+.01*(m-.5);y=F(2.,x);if(y>-5&&y<5){ if(n==0){M(x,y) n=1;}else L(x,y)} else n=0;} fprintf(o,".03 W 0 1 0 RGB S\n"); |
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+ | n=0;DO(m,1001){x=-5.+.01*(m-.5);y=F(1.,x);if(y>-5&&y<5){ if(n==0){M(x,y) n=1;}else L(x,y)} else n=0;} fprintf(o,".03 W 0 1 0 RGB S\n"); |
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+ | DO(k,20){ t=-2.+.1*k; |
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+ | n=0;DO(m,1001){x=-5.+.01*(m-.5);y=F(t,x);if(y>-7.2&&y<7.2){ if(n==0){M(x,y) n=1;}else L(x,y)} else n=0;} fprintf(o,".01 W 0 0 0 RGB S\n"); |
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+ | } |
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+ | fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%'); |
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+ | fclose(o); |
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+ | system("epstopdf frac1z.eps"); |
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+ | system( "open frac1z.pdf"); |
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+ | } |
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+ | </nowiki></poem> |
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==[[Latex]] generator of labels== |
==[[Latex]] generator of labels== |
Revision as of 18:41, 26 August 2013
Iterates of function $T(z)=-1/z$
$y=T^n(x)$ is plotted versus $x$ for various real values of number $n$ of iteration.
The non-integer iterates of function $T$ are evaluated using the superfunction
$\displaystyle F(z)=\tan\left(\frac{2}{\pi} z\right)$
and the Abel function
$\displaystyle G(z)=F^{-1}(z)=\frac{2}{\pi} \arctan\left( z\right)$
C++ generator of curves
File ado.cin should be loaded to the working directory in order to compile the C++ code below.
#include<math.h>
#include<stdio.h>
#include<stdlib.h>
#define DO(x,y) for(x=0;x<y;x++)
#define DB double
#include"ado.cin"
DB F(DB n,DB x){return tan( (M_PI/2)*n+ atan(x));}
main(){ FILE *o; int m,n,k; DB x,y,t;
o=fopen("frac1z.eps","w");
ado(o,1002,1002);
#define M(x,y) fprintf(o,"%7.4f %7.4f M\n",0.+x,0.+y);
#define L(x,y) fprintf(o,"%7.4f %7.4f L\n",0.+x,0.+y);
fprintf(o,"501 501 translate 100 100 scale 2 setlinecap\n");
for(n=-5;n<6;n++) { M(-5,n)L(5,n)}
for(m=-5;m<6;m++) { M(m,-5)L(m,5)}
fprintf(o,".005 W S\n");
M(-5,0)L(5,0)
M(0,-5)L(0,5)
fprintf(o,".02 W S\n");
n=0;DO(m,1001){x=-5.+.01*(m-.5);y=F(2.,x);if(y>-5&&y<5){ if(n==0){M(x,y) n=1;}else L(x,y)} else n=0;} fprintf(o,".03 W 0 1 0 RGB S\n");
n=0;DO(m,1001){x=-5.+.01*(m-.5);y=F(1.,x);if(y>-5&&y<5){ if(n==0){M(x,y) n=1;}else L(x,y)} else n=0;} fprintf(o,".03 W 0 1 0 RGB S\n");
DO(k,20){ t=-2.+.1*k;
n=0;DO(m,1001){x=-5.+.01*(m-.5);y=F(t,x);if(y>-7.2&&y<7.2){ if(n==0){M(x,y) n=1;}else L(x,y)} else n=0;} fprintf(o,".01 W 0 0 0 RGB S\n");
}
fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%');
fclose(o);
system("epstopdf frac1z.eps");
system( "open frac1z.pdf");
}
Latex generator of labels
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 18:37, 26 August 2013 | 2,089 × 2,089 (734 KB) | T (talk | contribs) | Iterates of function $T(z)=-1/z$ $y=T^n(x)$ is plotted versus $x$ for various real values of number $n$ of iteration. The non-integer iterates of function $T$ are evaluated using the superfunction $\displaystyle F(z)=\tan\left(\frac{2}{\pi} z\r... |
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