hi! lately I'm thinking about animating complex phase portraits so I tried something like this:

restart;
with(plots);
f := (a, z) -> (z*a - 1)/(z^2 + z + 1);
display(seq(densityplot(proc(x, y) local res; res := evalhf(argument(f(1/100*a, y + x*I))); return res; end proc, -4 .. 4, -4 .. 4, axes = boxed, view = [-2 .. 2, -2 .. 2], restricttoranges, colorstyle = HUE, style = surface, grid = [201, 201]), a = 1 .. 200), insequence = true);
 

but this takes a long time to load. Do you how can we optimizate this code?

hi, do you know how can we plot analogy situation from this post:

https://mathematica.stackexchange.com/questions/100051/dynamic-epicycles/100108#100108

I really like simplicity and beauty of the idea from:

https://www.mapleprimes.com/posts/206167-Procedures-For-Two-Animations

and I wonder if it would be possible to add a third rolling circle similarly not including such long code from first page.

thanks in advance

hi, is there any option to make inequality in animate with filled/marked area?

restart;
with(plots);
display(animate(implicitplot, [abs(x + y*I - a) <= 2*(1 - abs(x + y*I)), x = -2 .. 2, y = -2 .. 2], a = -1.75 .. 1.75, frames = 100), implicitplot(x^2 + y^2 = 1, x = -2 .. 2, y = -2 .. 2, color = black));

hi, do you know how to use discont in this plot? (is it even possible?)

restart;
with(plots);
animate(implicitplot, [y^2 = x^3/(2*a - x), x = -5 .. 5, y = -5 .. 5], a = -5 .. 5);
 

hi I want to map these two phase portraits on sphere according.

Upper hemisphere:

Lower hemisphere:

I used code from this post

https://www.mapleprimes.com/posts/136598-Images-On-Surfaces

but I can't figure out how to delete this black half and add next part:

I found this idea in Elias Wegert's book Visual Complex Functions. Thanks in advance.