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principal.c
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principal.c
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/*
c console program
computes q angles of external rays landing on the principal Misiurewicz point
of the wake p/q
https://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/p_misiurewicz
input:
* p/q
* b = denomintor of smaller farey parent of p/q = step n of the shift map : n = n + dn; dn < length; it is also remainder of div (n , Length);
* 2 angles of the wake p/q in the form of binary formatted strings of lentgh q:
Relation between input strings and angles of the wake:
** sM -> 0.(sM)
** sP -> 0.(sP)
output:
* q angles of the principal Misiurewicz point of the wake p/q in the form of binary formatted strings
notes/ to do:
* wake angles can be computed from the p/q
===================================
gcc principal.c -Wall
./a.out
./a.out > p.txt
----------
~/c/string/shift/preper/p7
======================
p/q = 2/5 b=3
(01001) lower wake = S-
01001(01010)
01001(10010)
01001(10100)
01010(00101)
01010(01001)
(01010) = S+ = higher wake
========================
p/q = 1/4 b=1
(0001) lower wake = S-
0001(0010)
0001(0100)
0001(1000)
0010(0001)
(0010) = S+ = higher wake
===================
p/q = 1/31 b=1
(0000000000000000000000000000001) lower wake = S-
0000000000000000000000000000001(0000000000000000000000000000010)
0000000000000000000000000000001(0000000000000000000000000000100)
0000000000000000000000000000001(0000000000000000000000000001000)
0000000000000000000000000000001(0000000000000000000000000010000)
0000000000000000000000000000001(0000000000000000000000000100000)
0000000000000000000000000000001(0000000000000000000000001000000)
0000000000000000000000000000001(0000000000000000000000010000000)
0000000000000000000000000000001(0000000000000000000000100000000)
0000000000000000000000000000001(0000000000000000000001000000000)
0000000000000000000000000000001(0000000000000000000010000000000)
0000000000000000000000000000001(0000000000000000000100000000000)
0000000000000000000000000000001(0000000000000000001000000000000)
0000000000000000000000000000001(0000000000000000010000000000000)
0000000000000000000000000000001(0000000000000000100000000000000)
0000000000000000000000000000001(0000000000000001000000000000000)
0000000000000000000000000000001(0000000000000010000000000000000)
0000000000000000000000000000001(0000000000000100000000000000000)
0000000000000000000000000000001(0000000000001000000000000000000)
0000000000000000000000000000001(0000000000010000000000000000000)
0000000000000000000000000000001(0000000000100000000000000000000)
0000000000000000000000000000001(0000000001000000000000000000000)
0000000000000000000000000000001(0000000010000000000000000000000)
0000000000000000000000000000001(0000000100000000000000000000000)
0000000000000000000000000000001(0000001000000000000000000000000)
0000000000000000000000000000001(0000010000000000000000000000000)
0000000000000000000000000000001(0000100000000000000000000000000)
0000000000000000000000000000001(0001000000000000000000000000000)
0000000000000000000000000000001(0010000000000000000000000000000)
0000000000000000000000000000001(0100000000000000000000000000000)
0000000000000000000000000000001(1000000000000000000000000000000)
0000000000000000000000000000010(0000000000000000000000000000001)
(0000000000000000000000000000010) = S+ = higher wake
*/
#define _GNU_SOURCE // asprintf
#include <stdio.h>
#include <stdlib.h>
#include <string.h> // strlen
/*
C substring function: It returns a pointer to the substring
https://www.programmingsimplified.com/c/source-code/c-substring
C substring program using pointers
To find substring we create a substring function which returns a pointer to string. String address, required length of substring and position from where to extract substring are the three arguments passed to function.
*/
char *substring(char *string, int position, int length)
{
char *pointer;
int c;
pointer = malloc(length+1); // remember to free
if (pointer == NULL)
{
printf("Unable to allocate memory.\n");
exit(1);
}
for (c = 0 ; c < length ; c++)
{
*(pointer+c) = *(string+position-1);
string++;
}
*(pointer+c) = '\0';
return pointer;
}
// shifting N places left
char *LeftShift(char *sIn, int n){
// lengthIn = length1+length2
int lengthIn= strlen(sIn);
int length1 = n;
int length2 = lengthIn - n+1 ;
// sIn = s1s2
char *s1 = substring(sIn,1, length1);
char *s2 = substring(sIn,n+1, length2 );
//
//printf("s1\t %s\n", s1);
//printf("s2\t %s\n", s2);
// sOut = shift(sIn, n) = s2s1
char *sOut = "";
asprintf(&sOut, "%s%s", s2, s1);
return sOut;
}
/*
find q angles of rays landing on the principal Misiurewicz point of the wake p/q
https://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/p_misiurewicz
input wake :
- wake angle p/q
- denominator of lower Farey parent of p/q
- angles : sM sPer
*/
int AnglesOfPrincipalMisiurewicz(int p, int q, int b, char *sM, char *sP){
// sOut = sOutPre(sOutPer)
char *sPre ; // setting for the first ray
char *sPer ;
//
int n;
int j;
printf("p/q = %d/%d\tb=%d\n\n", p, q, b); // input
printf("(%s)\t lower wake = S-\n", sM); // lower wake = (S-)
//
printf("%s(%s)\n",sM, sP); // angle of the first Misiurewicz ray
//
for (j = 1; j< q-1; j++){ // there are q rays ( from 0 to q-1), first and last rays are out the loop
n = (j*b) % q;
// sPre
if (j< q-p)
{ sPre = sM;}
else { sPre = sP;}
//
sPer = LeftShift(sP,n);
// sOut
printf("%s(%s)\n",sPre, sPer );
}
printf("%s(%s)\n",sP, sM); // angle of the last (q-1) Misiurewicz ray
printf("(%s)\t = S+ = higher wake \n", sP); //
return 0;
}
// test if input is good
//
int BadInput(int p, int q, int b, char *sM, char *sP ){
if ( // length of each string should be q
strlen(sP) != q ||
strlen(sM) != q ||
// only positive integers
b<0 ||
p<0 ||
q<0 ||
p>q // only proper fraction
) { return 1;}
return 0; // OK
}
// ===========================================================
int main(){
/*
examples:
p q b sM sP
1 4 1 0001 0010
1 31 1 0000000000000000000000000000001 0000000000000000000000000000010
34 89 55 01001010010010100101001001010010010100101001001010010100100101001001010010100100101001001 01001010010010100101001001010010010100101001001010010100100101001001010010100100101001010
*/
// p/q : p< q ; p>0 and q>0
int p = 34;
int q = 89;
// denomintor of smaller farey parent of p/q
// step n of the shift map : n = n + dn; dn < length; it is also remainder of div (n , Length);
int b = 55; // b < q
// = angles of 2 wake rays: sM < sP
// length of each string = q
char *sM = "01001010010010100101001001010010010100101001001010010100100101001001010010100100101001001"; // S- = smaller
char *sP = "01001010010010100101001001010010010100101001001010010100100101001001010010100100101001010"; // S+ = higher
// check input
if (BadInput(p,q,b,sM,sP))
{printf("bad input \n"); return 1;}
//
AnglesOfPrincipalMisiurewicz(p,q,b,sM,sP);
return 0;
}