Sterling2 Fractal Formulas

/////////////////////////////////////

// ftloo01.c

// stephen c. ferguson

// created 10/18/98

// modified August 2008 by Tad Boniecki

/////////////////////////////////////

// 3358 - 3418

void Formula_00(CDATA *v)

{

// Nova variation method

z = v->z;

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

sine_cosine();

z2 = z*z;

z3 = z2*z;

v->z = z - (zsin*clog_z() - ctan_z())/(z2*zcos - 2*z)* v->c;

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// 3243 - 3258

void Formula_01(CDATA *v)

{

// Nova variation method

z = v->z;

//v->z += 1;

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

sine_cosine();

z2 = z*z;

z3 = z2*z;

v->z = z-(z3*zsin - 1)/(7*z2*zcos - 1)+ v->c; //

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// very similar to #6

void Formula_02(CDATA *v)

{

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

v->z = z-(zsin/(1e-15+zcos))*(z8-z6-zsin-z-1)/(8*z7-6*z5-zcos -c); // almost the old 49 for 3165 "no 1-3"

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 3189 - 3197, and 3199 - 3205 a very complicated one

void Formula_03(CDATA *v)

{

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z3*z;

z5 = z4*z;

sine_cosine();

//zcos = (1e-15+zcos)/0.1;

//zsin = (1e-15+zsin)/0.1;

v->z = z - ((z*zsin) - z3 + v->c/(z5*zcos))/(c/z5 + zsin*zcos - 100*z5);

v->z = v->z - z*((z4 - z*zsin - v->c)/(4*z3 - 3*z2 - 2*z - z*zcos - v->c));

v->z = c/(v->z);

v->z = (v->z)*(v->z) - v->z;

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 3045 - 3077

void Formula_04(CDATA *v)

{

// Newton method

if (v->jul == 0)

v->z = 1;

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

z = z1 = v->z;

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

sine_cosine();

//v->z = z-(z4-z)/(4*z3)+v->c;

// a good one

v->z = z - ((z5 - z4 + z3*zsin + v->c)/(z4 + z3 - z2*zcos + v->c));

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 3003 - 3044

void Formula_05(CDATA *v)

{

// Twister weed method

z1 = z;

z = v->z;

c2 = cexp_z();

//z = z1;

//c2 = 1;

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

z1 = z;

v->pXTemp[v->Iteration] = __real__ z;

v->pYTemp[v->Iteration] = __imag__ z;

z2 = z*z;

sine_cosine();

z = z -(c2*z2*z2-1)/(z*z2*zcos - z*c)+ v->c;

zd = z1-z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ z;

v->pYTemp[v->Iteration] = __imag__ z;

v->z = z;

}

// another variant of old #49, ?? 3167 - 3174 Others too - it's good

void Formula_06(CDATA *v)

{

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

//v->z = z-(zsin/(1e-15+zcos))*(z8-z6-zsin-z-1)/(8*z7-6*z5-zcos -c); // almost the old 49 for 3165 "no 1-3"

//v->z = z-(zsin/(1e-15+zcos))*(z8-zsin-z*c)/(8*z7-zcos-c); // current #8 - same red/blue flame as the above when enlarged

v->z = z-(zsin/(1e-15+zcos))*(z8-z6-zsin-z-1)/(8*z7-6*z5-zcos); // new 3167 - 3174 ?

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 2946 - 2987

void Formula_07(CDATA *v) // Phoenix

{

// Nova variation method

z = v->z;

v->z = csin_z();

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

sine_cosine();

v->z = z -(c*cexp_z()*z4-z)*(z3 - zsin*clog_z())/(z2*zcos + zsin*zsin*zsin)+v->c;

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// variant of old #49, 3152 to 3163

void Formula_08(CDATA *v)

{

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

v->z = z-(zsin/(1e-15+zcos))*(z8-zsin-z*c)/(8*z7-zcos-c);

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 2848 - 2872

void Formula_09(CDATA *v)

{

// Nova variation method

z = v->z;

v->z = csin_z();

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

sine_cosine();

//v->z = z-(z4-z)/(4*z3-z)+ v->c;

v->z = z-(z3 - zsin*clog_z())/(z2*zcos + zsin*zsin*zsin)+v->c;

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 2719 - 2809

void Formula_10(CDATA *v)

{

// Nova variation method

z = v->z;

//v->z += 1;

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

sine_cosine();

z2 = z*z;

z3 = z2*z;

v->z = z-(z3*zsin-1)/(3*z2*zcos - zsin*zsin)+v->c;

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

//OK 2698 - 2718

void Formula_11(CDATA *v)

{

z = v->z;

c = v->c;

z = -z/3;

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ z;

v->pYTemp[v->Iteration] = __imag__ z;

z2 = z;

z1 = z*z;

sine_cosine();

z = z - (c*cexp_z()*zsin * z1*clog_z())/(z*z + c * zcos);

zd = z-z2;

temp = sum_sqrs_zd();

}

__real__ v->z = __real__ z;

__imag__ v->z = __imag__ z;

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 2652 - 2687

void Formula_18(CDATA *v) // Newton M-Set, Explanation by Paul Carlson

{

z = v->z;

c = v->c;

z = -z/3;

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ z;

v->pYTemp[v->Iteration] = __imag__ z;

z2 = z;

z1 = z*z;

sine_cosine();

//z=z-(z*z1+z1*c-z+c-zsin)/(3*z1+2*c*z-1-zcos);

z= z - (c*cexp_z()*zsin - z1*clog_z())/(z*z + c*z - zcos);

zd = z-z2;

temp = sum_sqrs_zd();

}

__real__ v->z = __real__ z;

__imag__ v->z = __imag__ z;

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 2620 - 2651

void Formula_19(CDATA *v)

{

z = v->z;

c = v->c;

z = -z/3;

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ z;

v->pYTemp[v->Iteration] = __imag__ z;

z2 = z;

//ztan = ctan_z()/v->bailout;

sine_cosine();

zcos = (1e-15+zcos)/v->dStrands;

zsin = (1e-15+zsin)/v->dStrands;

z=z-(z*z*z+ c*cexp_z() - z - z*clog_z())/(3*z*z+2*c*z-zcos);

zd = z-z2;

temp = sum_sqrs_zd();

}

__real__ v->z = __real__ z;

__imag__ v->z = __imag__ z;

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 2599 - 2619

void Formula_20(CDATA *v)

{

Solve the roots of the function.

Initialize z to one of the roots.

Apply Newton's method for solving roots.

f(z) = z - z/z'

z = z*z*z*z - z*z*z*c - z - c; // the function

z' = 4*z*z*z - 3*z*z*c - 1; // 1st derivative

z'' = 12*z*z - 6*z*c; // 2nd derivative

12*z*z = 6*z*c;

z = (6*z*c)/(12*z); // solve for z

z = c/2;

z = v->z;

c = v->c;

z = z/2;

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ z;

v->pYTemp[v->Iteration] = __imag__ z;

z2 = z;

z1 = z*z;

sine_cosine();

//zcos = (1e-15+zcos)/v->dStrands;

//zsin = (1e-15+zsin)/v->dStrands;

z=z-(z1*c*cexp_z() - z1*z*c - z - z*clog_z())/(4*z*z1 - 3*z1*c - zcos);

zd = z-z2;

temp = sum_sqrs_zd();

}

__real__ v->z = __real__ z;

__imag__ v->z = __imag__ z;

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 2584 - 2598

void Formula_21(CDATA *v) //

{

Solve the roots of the function.

Initialize z to one of the roots.

Apply Newton's method for solving roots.

f(z) = z - z/z'

z = z*z*z*c + z*z + z + c; // the function

z' = 3*z*z*c + 2*z + 1; // 1st derivative

z'' = 6*z*c + 2; // 2nd derivative

6*z*c = -2;

z = -2/(6*c); // solve for z

z = -1/(3*c)

z = v->z;

c = v->c;

z = -1/(3*z);

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ z;

v->pYTemp[v->Iteration] = __imag__ z;

z2 = z;

z1 = z*z;

sine_cosine();

z =z-(z1*c + c*cexp_z() + ctan_z() - zcos)/(z1*z1*c + z*clog_z() + c - zsin);

zd = z-z2;

temp = sum_sqrs_zd();

}

__real__ v->z = __real__ z;

__imag__ v->z = __imag__ z;

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 2550 to 2583

void Formula_22(CDATA *v) //

{

z = v->z;

c = v->c;

if (v->jul == 0)

z = -.5;

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ z;

v->pYTemp[v->Iteration] = __imag__ z;

z2 = z;

z1 = z*z;

z = z2;

sine_cosine();

z = z-(z1*z*c * c * cexp_z()*zsin)/(zsin + 2*zcos);

zd = z-z2;

temp = sum_sqrs_zd();

}

__real__ v->z = __real__ z;

__imag__ v->z = __imag__ z;

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 2511 - 2542

void Formula_23(CDATA *v) //

{

z = v->z;

c = v->c;

z = -.5/z;

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ z;

v->pYTemp[v->Iteration] = __imag__ z;

z2 = z;

z1 = z*z;

//ztan = ctan_z();

sine_cosine();

//zcos = (1e-15+zcos)/v->dStrands;

//zsin = (1e-15+zsin)/v->dStrands;

z = z-(z1*z1*c + z1*z + z + c - zsin)/(4*z1*z*c + 3*cexp_z() - zcos);

zd = z-z2;

temp = sum_sqrs_zd();

}

__real__ v->z = __real__ z;

__imag__ v->z = __imag__ z;

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 2479 - 2510

void Formula_24(CDATA *v) // testing

{

Solve the roots of the function.

Initialize z to one of the roots.

Apply Newton's method for solving roots.

f(z) = z - z/z'

z = z*z*z + z*z*c + c; // the function

z' = 3*z*z + 2*z*c ; // 1st derivative

z'' = 6*z + 2*c ; // 2nd derivative

6*z = -2*c;

z = -2*c/6;

z = v->z;

c = v->c;

z = -z/3;

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ z;

v->pYTemp[v->Iteration] = __imag__ z;

z2 = z;

z1 = z*z;

//ztan = ctan_z();

sine_cosine();

//zcos = (1e-15+zcos)/v->dStrands;

//zsin = (1e-15+zsin)/v->dStrands;

z = z - (z1*cexp_z() + z1*c + c - zsin)/(3*z1 + 2*z*c - zcos);

zd = z-z2;

temp = sum_sqrs_zd();

}

__real__ v->z = __real__ z;

__imag__ v->z = __imag__ z;

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 2449 - 2478

void Formula_25(CDATA *v) // testing

{

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

v->z = z + (z5*zsin - c*z4*zcos)/((z5*clog_z() + ctan_z()) * ctan_z());

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 2434 - 2448

void Formula_26(CDATA *v) // testing

{

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

v->z = z + cexp_z() * (z5*zsin - c*z4*zcos)/((z5*clog_z() + ctan_z()) * ctan_z());

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK but not too hot 2421 - 2433

void Formula_27(CDATA *v) // testing

{

Solve the roots of the function.

Initialize z to one of the roots.

Apply Newton's method for solving roots.

f(z) = z - z/z'

z = z*z*z*z*z*z*z + z*z*z*z*z*z*c + c; // the function

z' = 7*z*z*z*z*z*z + 6*z*z*z*z*z*c ; // 1st derivative

z'' = 42*z*z*z*z*z + 30*z*z*z*z*c ; // 2nd derivative

42*z*z*z*z*z = -30*z*z*z*z*c;

z = -(30*z*z*z*z*c)/(42*z*z*z*z);

z = -(15*c)/21;

z = -(5*c)/7;

//if (jul == 0)

z = v->z;

c = v->c;

z = -(5*z)/7;

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ z;

v->pYTemp[v->Iteration] = __imag__ z;

z1 = z;

z2 = z1*z1;

z5 = z2*z2*z1;

sine_cosine();

//zcos = (1e-15+zcos)/v->dStrands;

//zsin = (1e-15+zsin)/v->dStrands;

z = (7*z5*z1 + 6*z5*c - zcos);

z = z1-(z5*z2 + z5*z1*c + c - zsin)/z;

v->z = z + ctan_z() * (z5*zsin - z4*zcos)/(z5 + ctan_z()) * zsin * zcos * ctan_z();

zd = z-z1;

temp = sum_sqrs_zd();

}

__real__ v->z = __real__ z;

__imag__ v->z = __imag__ z;

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 2405 to 2420

void Formula_28(CDATA *v) // 9th order Newton Mset

{

Solve the roots of the function.

Initialize z to one of the roots.

Apply Newton's method for solving roots.

f(z) = z - z/z'

z = z*z*z*z*z*z*z*z*z + z*z*z*z*z*z*z*z*c + c; // the function

z' = 9*z*z*z*z*z*z*z*z + 8*z*z*z*z*z*z*z*c ; // 1st derivative

z'' = 72*z*z*z*z*z*z*z + 56*z*z*z*z*z*z*c ; // 2nd derivative

72*z*z*z*z*z*z*z = -56*z*z*z*z*z*z*c;

z = -(56*z*z*z*z*z*z*c)/(72*z*z*z*z*z*z);

z = -(7*c)/9;

//if (jul == 0)

z = v->z;

c = v->c;

z = -(7*z)/9;

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ z;

v->pYTemp[v->Iteration] = __imag__ z;

z1 = z;

z2 = z*z;

z4 = z2*z2;

z5 = z2*z2*z;

z8 = z4*z4;

sine_cosine();

//zcos = (1e-15+zcos)/v->dStrands;

//zsin = (1e-15+zsin)/v->dStrands;

//z = z-(z5*z4 + z8*c + c - zsin)/(9*z8 + 8*z5*z2*c - zcos);

z = z - zsin/(clog_z()*z8 + (cexp_z() + c*z - zcos));

zd = z-z1;

temp = sum_sqrs_zd();

}

__real__ v->z = __real__ z;

__imag__ v->z = __imag__ z;

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 2386 to 2404

void Formula_29(CDATA *v) // 13th order Newton Mset

{

Solve the roots of the function.

Initialize z to one of the roots.

Apply Newton's method for solving roots.

f(z) = z - z/z'

z = z^13 + (z^12)*c + c; // the function

z' = 13*(z^12) + 12*(z^11)*c; // 1st derivative

z'' = 12*13*(z^11) + 11*12*(z^10)*c; // 2nd derivative

12*13*(z^11) = -11*12*(z^10)*c;

z = -(11*12*(z^10)*c)/(12*13*(z^10));

= -(11*12*c)/(12*13);

= -11*c/13;

//if (jul == 0)

z = v->z;

c = v->c;

z = -(11*z)/13;

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ z;

v->pYTemp[v->Iteration] = __imag__ z;

z1 = z;

z2 = z*z;

z4 = z2*z2;

z5 = z2*z2*z;

z8 = z4*z2;

z8 = z4;

sine_cosine();

//zcos = (1e-15+zcos)/v->dStrands;

//zsin = (1e-15+zsin)/v->dStrands;

z = z - (clog_z()*z8 + (cexp_z() + c*z - zcos))/zsin;

zd = z-z1;

temp = sum_sqrs_zd();

}

__real__ v->z = __real__ z;

__imag__ v->z = __imag__ z;

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 2364 to 2380

void Formula_30(CDATA *v) // Testing again

{

z = v->z;

c = v->c;

z = -(3*z)/5;

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ z;

v->pYTemp[v->Iteration] = __imag__ z;

z1 = z;

z2 = z*z;

sine_cosine();

//zcos = (1e-15+zcos)/v->dStrands;

//zsin = (1e-15+zsin)/v->dStrands;

z = z - clog_z()*(z2*z2*z + z2*z2*c + z + c - zsin)/(5*z2*cexp_z() + 4*z2*z*c + 1 - zcos);

zd = z-z1;

temp = sum_sqrs_zd();

}

__real__ v->z = __real__ z;

__imag__ v->z = __imag__ z;

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 2311 to 2341

void Formula_31(CDATA *v) // Newton Diamond

{

Solve the roots of the function.

Initialize z to one of the roots.

Apply Newton's method for solving roots.

f(z) = z - z/z'

z = z^5 + (z^4)*c + z + c; // the function

z' = 5*(z^4) + 4*(z^3)*c + 1; // 1st derivative

z'' = 20*(z^3) + 12*(z^2)*c; // 2nd derivative

20*(z^3) = -12*(z^2)*c;

z = -(12*(z^2)*c)/(20*(z^2)); // solve for z

z = -(3*c)/5;

z = v->z;

c = v->c;

z = -(3*z)/5;

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ z;

v->pYTemp[v->Iteration] = __imag__ z;

z1 = z;

z2 = z*z;

sine_cosine();

//zcos = (1e-15+zcos)/v->dStrands;

//zsin = (1e-15+zsin)/v->dStrands;

z = z - clog_z()*(z2*z2*z + z2*z2*c + z + c - zsin)/(5*z2*z2 + 4*z2*z*c + 1 - zcos);

zd = z-z1;

temp = sum_sqrs_zd();

}

__real__ v->z = __real__ z;

__imag__ v->z = __imag__ z;

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// ok 2283 to 2310

void Formula_32(CDATA *v) // Newton Pentagon

{

Solve the roots of the function.

Initialize z to one of the roots.

Apply Newton's method for solving roots.

f(z) = z - z/z'

z = z^6 + (z^5)*c + z + c; // the function

z' = 6*(z^5) + 5*(z^4)*c + 1; // 1st derivative

z'' = 30*(z^4) + 20*(z^3)*c; // 2nd derivative

30*(z^4) = -20*(z^3)*c;

z = -(20*(z^3)*c)/(30*(z^3)); // solve for z

z = -(2*c)/3;

z = v->z;

c = v->c;

z = -(2*z)/3;

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ z;

v->pYTemp[v->Iteration] = __imag__ z;

z1 = z;

z2 = z*z;

z4 = z2*z2;

sine_cosine();

//zcos = (1e-15+zcos)/v->dStrands;

//zsin = (1e-15+zsin)/v->dStrands;

//z=z-(z4*z2 + z4*z*c + z + c - zsin)/(6*z4*z + 5*z4*c - zcos);

z = z - z2*cexp_z()+ c*zcos;

zd = z-z1;

temp = sum_sqrs_zd();

}

__real__ v->z = __real__ z;

__imag__ v->z = __imag__ z;

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 2270 to 2282

void Formula_33(CDATA *v) // Newton Hexagon

{

Solve the roots of the function.

Initialize z to one of the roots.

Apply Newton's method for solving roots.

f(z) = z - z/z'

z = z^7 + (z^6)*c + z + c; // the function

z' = 7*(z^6) + 6*(z^5)*c + 1; // 1st derivative

z'' = 42*(z^5) + 30*(z^4)*c; // 2nd derivative

42*(z^5) = -30*(z^4)*c;

z = -(30*(z^4)*c)/(42*(z^4)); // solve for z

z = -(5*c)/7;

z = v->z;

c = v->c;

z = -(5*z)/7;

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ z;

v->pYTemp[v->Iteration] = __imag__ z;

z1 = z;

z2 = z*z;

z4 = z2*z2;

sine_cosine();

//zcos = (1e-15+zcos)/v->dStrands;

//zsin = (1e-15+zsin)/v->dStrands;

z = z - (z4*z2*z + z4*z2*c + z*cexp_z() + c - zsin)/(7*z4*z2 + 6*z4*z*c + cexp_z()* - zcos);

zd = z-z1;

temp = sum_sqrs_zd();

}

__real__ v->z = __real__ z;

__imag__ v->z = __imag__ z;

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 2257 to 2269

void Formula_34(CDATA *v) // Newton Octagon

{

Solve the roots of the function.

Initialize z to one of the roots.

Apply Newton's method for solving roots.

f(z) = z - z/z'

z = z^9 + (z^8)*c + z + c; // the function

z' = 9*(z^8) + 8*(z^7)*c + 1; // 1st derivative

z'' = 72*(z^7) + 56*(z^6)*c; // 2nd derivative

72*(z^7) = -56*(z^6)*c;

z = -(56*(z^6)*c)/(72*(z^6)); // solve for z

z = -(7*c)/9;

z = v->z;

c = v->c;

z = -(7*z)/9;

temp = 1;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ z;

v->pYTemp[v->Iteration] = __imag__ z;

z1 = z;

z2 = z*z;

z4 = z2*z2;

sine_cosine();

//zcos = (1e-15+zcos)/v->dStrands;

//zsin = (1e-15+zsin)/v->dStrands;

z=z- cexp_z()*(z4*z4*z + z4*z4*c + z + c - zsin)/(9*z4*z4 + 8*z4*z2*z*c + 1 - zcos);

zd = z-z1;

temp = sum_sqrs_zd();

}

__real__ v->z = __real__ z;

__imag__ v->z = __imag__ z;

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// keep 3147 to 3151

void Formula_35(CDATA *v) // Testing

{

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

v->z = z-(zsin/(1e-15+zcos))*(z7-zsin-z*c-1)/(8*z7-zcos-c);

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// keep 2207 to 2241

void Formula_36(CDATA *v)

{

//MessageBox(NULL, "formula 02", "bug", MB_OK);

//if (v->jul == 0)

//v->z += 1;

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

c2 = cexp_z();

v->z = z-(z5-z3-z2*zsin-c2*zsin)/(5*z3-z*z2-z2*zcos-1-zcos)+ v->c;

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 2193-2206

void Formula_37(CDATA *v)

{

//MessageBox(NULL, "formula 02", "bug", MB_OK);

//if (v->jul == 0)

//v->z += 1;

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

v->z = z + (ctan_z()*ctan_z() - z4 + 7*c )/((z*zsin * zcos - z5)*ctan_z());

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK 2184 to 2192

void Formula_38(CDATA *v)

{

//MessageBox(NULL, "formula 02", "bug", MB_OK);

//if (v->jul == 0)

//v->z += 1;

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

v->z = z - (z7*zcos - z4)/(z2*zsin -1 ) + v->c;

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// keep 2149 - 2171

void Formula_39(CDATA *v)

{

//MessageBox(NULL, "formula 02", "bug", MB_OK);

//if (v->jul == 0)

//v->z += 1;

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

v->z = z-(z3-z2-z*zsin)/(z3-z2-z*zcos)+v->c;

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// keep 2137 - 2148

void Formula_40(CDATA *v)

{

//MessageBox(NULL, "formula 02", "bug", MB_OK);

if (v->jul == 0)

v->z += 1;

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

v->z = z - (z - c)*(z + c)*(z*z + c)*c;

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// keep 2123-2134

void Formula_41(CDATA *v)

{

//MessageBox(NULL, "formula 02", "bug", MB_OK);

//if (v->jul == 0)

//v->z += 1;

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

v->z = z-(zsin/(1e-15+zsin))*(z8-z5*zsin-z*c-1)/(8*z7-6*z5-zcos-c)*(z5-z4*zsin-zsin*z*c-z);

// was v->z = z-(z5-z4*zsin-zsin*z*c-z)/(5*z4-5*z4*zcos-zcos*z*c-1);

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// OK but weak 3123 - 3135

void Formula_42(CDATA *v)

{

//MessageBox(NULL, "formula 02", "bug", MB_OK);

//if (v->jul == 0)

//v->z += 1;

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

v->z = z-(z3*zsin * zcos * zcos - c)/(z*cexp_z() - zsin + z2); // change this

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// Similar to original 3087 - 3095

void Formula_43(CDATA *v)

{

//MessageBox(NULL, "formula 02", "bug", MB_OK);

//if (v->jul == 0)

//v->z += 1;

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

v->z = z-(z5*zsin-z3*zsin-zsin*z*c-z)/(5*z4*zcos-z4*zcos-zcos*z2*c-1);

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// keep 2050 - 2070

void Formula_44(CDATA *v)

{

//MessageBox(NULL, "formula 02", "bug", MB_OK);

//if (v->jul == 0)

//v->z += 1;

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

// was v->z = z-(z6-z5-z5*zsin-z4*zsin*c-zsin*z*c-z)/(6*z5-5*z4-z5*zcos-z4*zcos*c-zcos*z*c-1);

v->z = z-(z5*zsin-z4*zsin-z3*zsin-z2*zsin*c)/(4*z3*zcos-3*z2*zcos-z2*zcos*c);

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// keep 2032-2049

void Formula_45(CDATA *v)

{

//MessageBox(NULL, "formula 02", "bug", MB_OK);

//if (v->jul == 0)

//v->z += 1;

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

v->z = (z -(z*zsin * zcos - z5)*ctan_z())/(zsin*z5 -zcos*(z2-zsin));

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// keep 1986 - 2028

void Formula_46(CDATA *v)

{

//MessageBox(NULL, "formula 02", "bug", MB_OK);

//if (v->jul == 0)

//v->z += 1;

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

v->z = z-(z8+z6+z5-z5*zsin-z4*zcos*c-z)/(8*z7-6*z5-5*z4-z5*zcos*zcos-z4*zcos-1);

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// keep 1957 - 1985

void Formula_47(CDATA *v)

{

//MessageBox(NULL, "formula 02", "bug", MB_OK);

//if (v->jul == 0)

//v->z += 1;

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

v->z = z - (c + ctan_z() + zcos*zsin)/(ctan_z() + z4*zsin - z5);

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// 1921 - 1930 keep

void Formula_48(CDATA *v)

{

//MessageBox(NULL, "formula 02", "bug", MB_OK);

//if (v->jul == 0)

//v->z += 1;

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

v->z = (z -(z*zsin * zcos - z5)*ctan_z()/(ctan_z()*ctan_z() - z4 + 7*c));

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// modified 20 June 2007 produced # 1696 - 1713; to keep

void Formula_49(CDATA *v)

{

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

v->z = z-(zsin/(1e-15+zcos*zsin + c))*(z8-z6-zsin-z*c-1)/(8*z7-6*z5-zcos-c);

// was v->z = z-(zsin/(1e-15+zcos))*(z8-z6-zsin-z*c-1)/(8*z7-6*z5-zcos-c);

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// modified June 2007; another version of #49; made # 1714 - 1733; To keep

void Formula_50(CDATA *v)

{

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

// was v->z = z-(z4-z3-z3-z2*zsin*c)/(4*z3-3*z2-z2*zcos*c);

v->z = z-(zsin/(1e-15+7*zcos*zsin + c))*(4*z8-z6-zsin-z*c-1)/(z7-6*z5-zcos-c);

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// entirely new formula 27/6/7; used for # 1737 - 1778; to keep

void Formula_51(CDATA *v)

{

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

// was v->z = z-(z4*zsin-z3*zsin-z3*zsin-z2*zsin*c)/(4*z3-3*z2-z2*zcos*c);

v->z = z - c*(z8*zsin - z5 + z4*zcos)/(z6 - 27*z7 + z*c);

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// entirely new formula 10/7/7; used for # 1800 - 1828; to keep

void Formula_52(CDATA *v)

{

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

// was v->z = z-(z4*zsin-z3*zsin-z3*zsin-z2*zsin*c)/(4*z3*zcos-3*z2*zcos-z2*zcos*c);

v->z = z - c*(z*ctan_z() - z4*zcos)/(zsin*z5 -zcos*(z2-zsin));

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// partially tested variant of new 52 22/7/7; 1837 - 1839 keep

void Formula_53(CDATA *v)

{

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

// was v->z = z-(z3*zsin-z2*zsin*c-1)/(3*z2*zcos-2*z*zcos*c);

v->z = z + ctan_z()*ctan_z();

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// 1847 - 1860

void Formula_54(CDATA *v)

{

//MessageBox(NULL, "formula 02", "bug", MB_OK);

// 4th order Nova

//if (v->jul == 0)

//v->z = 1;

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

v->z = z + ctan_z()*ctan_z() * (z + z*ctan_z()) * z2*zsin * z3*zcos * z8*ctan_z()/(z5*zsin - z4);

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}

// 1862 - 1903

void Formula_55(CDATA *v)

{

//MessageBox(NULL, "formula 02", "bug", MB_OK);

//if (v->jul == 0)

//v->z += 1;

temp = 1;

c = v->c;

while( v->Iteration++ < v->Maxit && temp > zerotol && temp < dMAX)

{

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

z = z1 = v->z;

z2 = z*z;

z3 = z2*z;

z4 = z2*z2;

z5 = z4*z;

z6 = z5*z;

z7 = z6*z;

z8 = z7*z;

sine_cosine();

v->z = z + ctan_z() * (z5 + ctan_z()) * zsin * zcos * ctan_z()/(z5*zsin - z4*zcos);

zd = z1-v->z;

temp = sum_sqrs_zd();

}

v->pXTemp[v->Iteration] = __real__ v->z;

v->pYTemp[v->Iteration] = __imag__ v->z;

}