@dharr 

It happens when I am so focussed on code editing that I cannot observe myself. If I type slowly everything is fine. It might have something to do with change equation labels, change of an index or deletion of some invisible characters.

The animation with the initial point is very instructive.

To be sure what I was looking at I did

implicitplot3d([f3], x1 = -a .. a, x2 = -a .. a, x3 = -a .. a, axes = normal, transparency = 0.7, numpoints = 5000, style = surface, color = [blue]);
plots[display](E3, %);

So the black dots are the solutions. At their locations the intersection curves of f1 with f2, f2 with f3 and f1 with f3 intersect. This would mean that at each solution 3 curves intersect or 6 curve segments meet. Is it possible to predict the number of segments without plotting them? Or the other way arround predict from the number and kind of intersecting curves the number of possible solutions?

Annother question I have: Sometimes, as here, there are infinite solutions. Infinite solutions mean a continutiy of points. Could it be that in the case that there are also infinite solutions, the  the pink curve locks into them. I.e. becomes itself a "continuous" solution.

@ecterrab 

I have just seen your reply by coincidence (I did not get a notification). Before I can reply in detail I have to solidify my landscape of physical principles. This will take time. I will see if I can dig out my old text books to verify whether they match other references. Its essential to have a common ground for discussion.

For the moment, I would like to thank you for your detailed reply

@ecterrab 

Excellent! Then I do not have to ask how to edit. Good that there is the Physics Updates project.

@Christian Wolinski 

I see

map(''`^`'', eqs, 2);
%;
            [^(a = b, 2), ^(c = d, 2), ^(e = f, 2)]

                  [ 2    2   2    2   2    2]
                  [a  = b , c  = d , e  = f ]

What you showed above, is it 2 times the same document opened in Maple 2020 and in Maple 2024?

What type of graphic document we are looking at?

Can you share a document with a drawing that shows the effect on your machine?

How does it look like if you change to print layout mode?

My guess is that something changed when Maple changed the Java IDE for the GUI, which happend from 2020 to 2021.

The GUI's of the two Maple versions should look different. Is that correct?

@Christian Wolinski 

Intersting detail. map  (a built-in function) must have undergone some changes.

Maple 2024

map(map@`^`, eqs, 2);
                  [ 2    2   2    2   2    2]
                  [a  = b , c  = d , e  = f ]

Maple 2020

map(map@`^`, eqs, 2);
Error, (in evalapply) invalid input: map expects 2 or more arguments, but received 1

Your variant works in both versions.

@Kitonum 

Thanks, for the work around. The use of ~ is only required for multiplication. Also here equations cannot not be treated the same way with arithmetic operators.

@acer @nm

On a faster machine (about 3 times on these specific worksheets) the effect is much less pronounced.

@acer 

It is only since I expanded animation frame count for continuous rendering in a recent worksheet.

I tested Maple 2023 with it. After execution (all animation were rendered expected) I could not edit anything at all. So Maple 2024 performs better but still not satisfactorily.

@nm 

Auto save is on 7 min.  I do not think that it is related to it because I can see when autosave is working and has finished.

@mmcdara 

Before running the 6 hours test I tried the other idea somehow: f1-f2 until f5-f1. The equations to be Fsolved became bulkier than the original ones.

Not a single root with

T := Isolate([seq(F[i], i = 1 .. 5)], [x1, x2, x3, x4, x5],maxroots=1,mthd=RC): j := nops(T);

I canceled after 6 hours.

@acer 

The ghost image was caused by an error of mine: p1 should have been removed from the display statement.

For the rest I can work around.

The loss of the red color of the cube is still an open point but not a road block at the moment.

Thank you
 

@acer 

Ok, it seems that the effect of jagged shading can be dampend by finding forgiving plot options. However "closed" surfaces (I mean generated over 2 Pi) show the artefact even with no color (context pannel No color, Light 4 and Transparency 0.25). If this is not a graphics card artefact, it is perhaps a numerical artefact (hardware floats?). Or a Maple algorithm could be improved in the respect. Neighboring facets of a continuous surface should not show such discontinuities.

I think I can work around this this time.

The more severe mudding: Rotating the plot reveals structures that should simply not be there. It looks like as if plots:-sphereplot (here sphere moved to 0.9)  has generated structures out of the plot range and hiden them by making them fully transparent. Plot with the option transparency let them appear again. Could this be?

PS.: I forgot to mention. Also in  https://www.mapleprimes.com/view.aspx?sf=305936_Answer/multiple_animations_02.mw a cube lost completely its red color.