I am primarily concerned with stardust4ever's variations: I'm guessing 90% of my fractal-related time involves either the Mandelbrot set or one of those ABS variations.

It was inspired by this:

https://fractalforums.org/fractal-mathematics-and-new-theories/28/naming-scheme-for-abs-variant-fractals/818GHN (General Hybridization Notation) works as follows:

The formula f(x,y) is the same as z = abs(z

^{y})

^{x/y} + z

_{0}. One of the members of fractals invented a folding function, which is applied here. x is the power, y is the number of "folds".

Let Mx be shorthand for z

^{x} + z

_{0}. This is short for Mandelbrot.

Let Bx be shorthand for abs(z)

^{x} + z

_{0}. This is the same as f(x,1). This is short for Burning Ship.

Let Fx be shorthand for abs(z

^{x}) + z

_{0}. This is the same as f(x,x). This is short for Buffalo.

If no x is given, it's assumed to be 2.

These capital letters are redundant, but they could speed things up.

If you have two pieces of a fractal (call them f

_{1} and f

_{2}), then [f

_{1},f

_{2}] is real(f

_{1}) + i*imag(f

_{2}).

The complex conjugate of any fractal in GHN is x' for a given fractal x.

Here's an example:

The 4th BS Partial Real Mandelbar is [B4,M4]'. We can break this down to a regular formula you can use in a program like Ultra Fractal:

(Real(B4) + Imag(M4)*i)' which is the same as:

(Real(B4) - Imag(M4)*i) which is the same as:

Real(abs(z)

^{4} + z

_{0}) - Imag(z

^{4} + z

_{0})*i which is the correct formula if you stick z = to the beginning.

All of Stardust4ever's twelve 2nd fractals are close to trivial with GHN. You can also raise a bracketed expression to a power and make a composition.

f

_{1}.f

_{2} means to do f2 to z and then f1, since you start inside and move out, as in parentheses. You put an exclamation point before f

_{1} or f

_{2} if you want to ignore z

_{0}.

What does the 4th Celtic Imaginary Quasi Perpendicular / Heart become?

I found out that iterating the 2nd order Perpendicular Buffalo without a z

_{0} followed by a 2nd order Buffalo with a z

_{0} gives this fractal. Here is what the GHN for this fractal is as well as the formula:

The Perpendicular Buffalo is a hybrid of the Buffalo and Perpendicular Burning Ship, or [F,[M,B]], while the Buffalo is just F. Since the P-Buffalo comes first, we have F.[F,[M,B]]. (remember, f1 goes inside). Since the Perpendicular Buffalo has no z0, the complete GHN formula for this fractal is:

F.![F,[M,B]].

Let's now convert this to a regular formula:

F.![F,(real(z

^{2} + z

_{0}) + imag(abs(z)

^{2} + z

_{0})*i)]

F.!(real(abs(z

^{2}) + z

_{0}) + imag(real(z

^{2} + z

_{0}) + imag(abs(z)

^{2} + z

_{0})*i)*i)

F.(real(abs(z

^{2})) + imag(real(z

^{2}) + imag(abs(z)

^{2})*i)*i)

abs((real(abs(z

^{2})) + imag(real(z

^{2}) + imag(abs(z)

^{2})*i)*i)

^{2}) + z

_{0}. (This happens because the formula to the right of the period acts like z.)

You can also use z

_{0}, +, -, *, /, all of the trig functions, etc. but they usually aren't necessary.

Linkback: https://fractalforums.org/fractal-mathematics-and-new-theories/28/a-way-to-make-certain-fractal-formulas-easy-to-understand/923/