Why does Fractal Formula "sin(z^2)-cos(z^2)+c" work with XaoS and not UltraFractal? - formula

Question

While using the real-time Fractal zoomer XaoS to explore the infinite universe having user formula "sin(z^2)-cos(z^2)+c", we start out here (important for universe identification and formula matching with other zoomer software applications, libraries or frameworks.):
I found the following fractal, which I really like:
As you, perhaps, can see, I have run up against the resolution wall (floor?), which means that the deeper I zoom at that point, the more pixelated and boxy the image gets:
Here is the XaoS source code (*.xpf file contents):
;Position file automatically generated by XaoS 4.2.1
; - a realtime interactive fractal zoomer
;Use xaos -loadpos <filename> to display it
(initstate)
(defaultpalette 0)
(formula 'user)
(usrform "sin(z^2)-cos(z^2)+c")
(angle 90)
(maxiter 1000)
(view -0.241140329885861603 1.09425325699643758E-015 8.78234117374088186E-014 8.78234139599431772E-014)
And Fractal->View... yields:
So I tried to enter the formula into UltraFractal, but no matter what I try, I can't get it to work.
This works:
init:
z = #start
loop:
z = sin(z^#power) + cos(z^#power) + #pixel
This does not work:
init:
z = #start
loop:
z = sin(z^#power) - cos(z^#power) + #pixel
The only difference in the above two is the minus sign.
This does not work:
init:
z = #start
loop:
z2p = z^#power
ss = sin(z2p)
cc = cos(z2p)
z = ss - cc + #pixel
This works:
init:
z = #start
loop:
z2p = z^#power
ss = sin(z2p)
cc = cos(z2p)
z = ss + cc + #pixel
but if I add a line negating cc, it doesn't work again:
init:
z = #start
loop:
z2p = z^#power
ss = sin(z2p)
cc = cos(z2p)
cc = -cc
z = ss + cc + #pixel
Finally, one last example.
This works:
init:
z = #start
loop:
z2p = z^#power
ss = sin(z2p)
cc = cos(z2p)
z = ss + 1 - ( 1 - cc ) + #pixel
but this doesn't:
init:
z = #start
loop:
z2p = z^#power
ss = sin(z2p)
cc = cos(z2p)
z = ss + 1 - ( 1 + cc ) + #pixel
As I think I've proven, negation and subtraction seem to be working. And I keep changing only the minus sign or the subtraction to make it stop working, so I suspect that there is a bug (or an arbitrary limitation of not being able to use this particular formula? - doesn't make sense.)
In the "Fractal Mode" pane, lower right part of screen, I click the third item down, "Switch Mode", and it displays "Contains errors." This is the only helpful feedback I've been able to find.
This is a paid program, so I do not expect to be having this problem. Anyone? (secondary question - what zoomer will render this well? Thanks!)
Here is my current UltraFractal source code:
comment {
This file contains standard fractal types for Ultra Fractal. Many of the
fractal formulas here were written by other formula authors, as noted in the
comments with each formula. All formulas have been edited and simplified by
Frederik Slijkerman.
These formulas are also available as objects for the common.ulb framework in
Standard.ulb.
}
sin2_minus_cos2 {
;
; Generic Mandelbrot set.
;
init:
z = #start
z9 = 1
loop:
z2p = z^#power
ss = sin(z2p)
cc = cos(z2p)
cc = -cc
z = ss + cc + #pixel
bailout:
|z| <= #bailout
$IFDEF VER60
perturbinit:
#dz = 0
perturbloop:
if #power == (2, 0)
#dz = 2 * #z * #dz + sqr(#dz) + #dpixel
elseif #power == (3, 0)
complex z2 = sqr(#z)
complex dz2 = sqr(#dz)
#dz = 3 * z2 * #dz + 3 * #z * dz2 + #dz * dz2 + #dpixel
else ; power 4
complex z2 = sqr(#z)
complex dz2 = sqr(#dz)
complex zdz4 = 4*#z*#dz
#dz = #dpixel + zdz4*z2 + 6*z2*dz2 + zdz4*dz2 + sqr(dz2)
endif
$ENDIF
default:
title = "sin2_minus_cos2"
center = (-0.5, 0)
$IFDEF VER50
rating = recommended
$ENDIF
$IFDEF VER60
perturb = #power == (2, 0) || #power == (3, 0) || #power == (4, 0)
$ENDIF
param start
caption = "Starting point"
default = (0,0)
hint = "The starting point parameter can be used to distort the Mandelbrot \
set. Use (0, 0) for the standard Mandelbrot set."
endparam
param power
caption = "Power"
default = (2,0)
hint = "This parameter sets the exponent for the Mandelbrot formula. \
Increasing the real part to 3, 4, and so on, will add discs to \
the Mandelbrot figure. Non-integer real values and non-zero \
imaginary values will create distorted Mandelbrot sets. Use (2, 0) \
for the standard Mandelbrot set."
endparam
float param bailout
caption = "Bailout value"
default = 4.0
min = 1.0
$IFDEF VER40
exponential = true
$ENDIF
hint = "This parameter defines how soon an orbit bails out while \
iterating. Larger values give smoother outlines; values around 4 \
give more interesting shapes around the set. Values less than 4 \
will distort the fractal."
endparam
switch:
type = "Julia"
seed = #pixel
power = power
bailout = bailout
}
I just punched the formula into a zoomer on my Android, and it seems to work.
Here is that coordinate, zoomed out just a little, so that you can barely see the pixelated fractal (just another example of great beauty from this wonderful infinite universe!):
EDIT:
This formula works:
init:
z = #start
loop:
; in XaoS, user formula sin(z)^2-cos(z)^2+c
z = sin(z)^2 - cos(z)^2 + #pixel
And here's the result in UltraFractal: