Efjh.cin

// the code below should be stored as efjh.cin in order to compile the generators of pictures (explicit plots and/or the complex maps) of the LogisticSequence. Sorry for use of global variables; in future I should try to avoid this. Kouznetsov 17:16, 16 October 2012 (JST).

DB Q=3; // defaul
DB LQ;
DB QQ,Q2,Q3,Q4,Q5,Q6,Q7;
DB C1,C2,C3,C4,C5,C6,C7;
DB S1,S2,S3,S4,S5,S6,S7,S8;

void maq(DB q){
Q=q;
QQ=Q*Q;
Q2=QQ;
Q3=QQ*Q;
Q4=QQ*QQ;
Q5=Q4*Q;
Q6=Q3*Q3;
Q7=Q6*Q;
LQ=log(Q);
C2=1.                                                           / (1.-Q) ;
C3=2.                                                           /((1.-Q)*(1.-Q2) );
C4=   (5.+Q)                                                    /((1.-Q)*(1.-Q2)*(1.-Q3) );
C5=2.*(7.+Q*(3.+Q*2.))                                          /((1.-Q)*(1.-Q2)*(1.-Q3)*(1.-Q4) );
C6=2.*(21.+Q*(14.+Q*(14.+Q*( 8.+Q*3.))))                        /((1.-Q)*(1.-Q2)*(1.-Q3)*(1.-Q4)*(1.-Q5));
C7=4.*(33.+Q*(30.+Q*(37.+Q*(32.+Q*(27.+Q*(12.+Q*(8.+Q)))))))    /((1.-Q)*(1.-Q2)*(1.-Q3)*(1.-Q4)*(1.-Q5)*(1.-Q6));
S1=1.;
S2=1.                                                           / (Q-1.);
S3=2.*Q                                                         /((Q-1.)*(Q2-1.));
S4=   Q *(1.+5.*Q*Q)                                            /((Q-1.)*(Q2-1.)*(Q3-1.) );
S5=2.*Q3*(3.+Q*(2.+QQ*7.))                                      /((Q-1.)*(Q2-1.)*(Q3-1.)*(Q4-1.) );
S6=2.*Q3*(1.+Q*(3.+QQ*(14.+Q*(14.+Q*(7.+QQ*21)))))              /((Q-1.)*(Q2-1.)*(Q3-1.)*(Q4-1.)*(Q5-1.));
S7=4.*Q4*(1.+Q*(5.+Q*(15.+Q*(12.+Q*(8.+Q*(30.+Q*(37.+Q*(27.+Q*(12.+QQ*(33.))))))))))
                                                               /((Q-1.)*(Q2-1.)*(Q3-1.)*(Q4-1.)*(Q5-1.)*(Q6-1.));
S8=Q4*(1.+QQ*(5.+Q*(60.+Q*(69.+Q*(89.+Q*(162.+Q*(415.+Q*(495.+Q*(531.+Q*(267.+Q*(630.+Q*(705.+Q*(621.+Q*(396+Q*(165.+Q*429)
             )     )      )      )      )       )       )       )       )       )       )       )       )
       )                                                       /((Q-1.)*(Q2-1.)*(Q3-1.)*(Q4-1.)*(Q5-1.)*(Q6-1.)*(Q7-1.));
;
printf("maq: Q=%9.6f\n",Q);}

z_type J(z_type z){ return .5-sqrt(.25-z/Q); }
z_type H(z_type z){ return Q*z*(1.-z); }

z_type f(z_type z){z_type e;e=exp(LQ*z);return e*(1.+e*(C2+e*(C3+e*(C4+e*(C5+e*(C6+e*C7))))));  }
z_type F(z_type z){     if(Re(z)>-6.) return H(F(z-1.));   return f(z);}
z_type e(z_type z){                     return z*(1.+z*(S2+z*(S3+z*(S4+z*(S5+z*(S6+z*(S7+z* S8)))))));}
z_type E(z_type z){     if(abs(z)>.1) return  E(J(z))+1.;   return log(e(z))/LQ;} 

//