Feel free to copy and paste any of these 26 formulas to check these fractals out for yourself!

Mandelbrot:
z=z^power + pixel;

Mandelbar Vertical:
z=conj(z^power + pixel);

Mandelbar Horizontal:
z=-conj(z^power + pixel);

Burning Ship:
z=abs(z^power + pixel);

Buffalo:
z=abs(z^power) + pixel;

BS Partial Imaginary:
z=real(z^power + pixel) + imag(abs(z^power + pixel))*flip(1);

BS Partial Real:
z=real(abs(z^power + pixel)) + imag(z^power + pixel)*flip(1);

BS Partial Real Mandelbar:
z=real(abs(z^power + pixel)) - imag(z^power + pixel)*flip(1);

Celtic:
z=real(abs(z^power) + pixel) + flip(1)*imag(z^power + pixel);

Celtic Mandelbar:
z=real(abs(z^power) + pixel) - flip(1)*imag(z^power + pixel);

Buffalo Partial Imaginary:
z=real(z^power + pixel) + flip(1)*imag(abs(z^power) + pixel);

Quasi Burning Ship:
z = real(abs(z^power + pixel)) + imag(abs(z^power) + pixel)*flip(1);

Celtic BS:
z = (abs(z)^power);
z = z - real(z) + abs(real(z)) + pixel;

Celtic BS Partial Imaginary:
z=(((real(z)) + abs(imag(z))*flip(1))^(power/2))^2;
z = z - real(z) + abs(real(z)) + pixel;

Celtic BS Partial Real:
z=(((real(abs(z))) + imag(z)*flip(1))^(power/2))^2;
z = z - real(z) + abs(real(z)) + pixel;

Celtic BS Partial Real Mandelbar:
z=(((real(abs(z))) + imag(z)*flip(1))^(power/2))^2;
z = z - real(z) + abs(real(z)) + pixel;
z = conj(z);

False Quasi Heart:
z=((real(abs(z)) + imag(z)*flip(1))^(power/2) + pixel)^2;

False Quasi Perpendicular:
z=((real(abs(z)) - imag(z)*flip(1))^(power/2) + pixel)^2;

Quasi Heart:
if (imag(z) > 0) {
z=abs(abs(z)^(power/2))^2 + pixel;
} else {
z=(abs(abs(z)^(power/-2))^-2 + pixel);
   
}

Quasi Perpendicular:
if (imag(z) < 0) {
z=abs(abs(z)^(power/2))^2 + pixel;
} else {
z=(abs(abs(z)^(power/-2))^-2 + pixel);
}

Imag Quasi Perpendicular / Heart:
if (imag(z) > 0) {      
z=abs(abs(z)^(power/2))^2 + pixel;      
} else {
z=(abs(abs(z)^(power/-2))^-2 + pixel);
}
z = flip(z);

Celtic False Quasi Heart:
z=((real(abs(z)) + imag(z)*flip(1))^(power/2));
z = (z - real(z) + abs(real(z)) + pixel)^2;

Celtic False Quasi Perpendicular:
z=((real(abs(z)) - imag(z)*flip(1))^(power/2));
z = (z - real(z) + abs(real(z)) + pixel)^2;

Celtic Quasi Heart:
if (imag(z) < 0) {
z=(conj(abs(abs(z)^(power))) + pixel);
} else {
z=((abs(abs(z)^(power))) + pixel);
}

Celtic Quasi Perpendicular:
if (imag(z) < 0) {
z=(conj(abs(abs(z)^(power))) + pixel);
} else {
z=((abs(abs(z)^(power))) + pixel);
}
z = conj(z);

Celtic Imaginary Quasi Perpendicular / Heart:
if (imag(z) < 0) {
z=(conj(abs(abs(z)^(power))) + pixel);
} else {
z=((abs(abs(z)^(power))) + pixel);
}
z = flip(z);

Linkback: https://fractalforums.org/chaospro/56/all-of-kosmic-stardusts-abs-variations/1317/

You're welcome! It took me over three years to figure these all out.

Sorry for the late reply.

I am finally registered here now. Feel free to use my formulas anytime. I am glad to see people enjoying them! 

Check out the recent KF feature of "auto-skew" for the abs() formulas.