Rotation Bifurcation...

[Chris M. Thomasson]

A strange bifurcation algorithm from an older iterated function system
of mine:

My pseudo code is in the description:

______________
// px_mutation interpolates from -4...4 across each frame; 1440 here.

render frames:
_________
// angle interpolates from 0...pi2 across iterations
// px = py = 0

// Iteration:
px = sin(angle * px_mutation);
py = cos(angle * py);
______________

Anybody should be able to reproduce it on their end. Right?

It's all 2d, but has a 3d vibe! Nice.

Any thoughts?

[sobriquet]

Post by Chris M. Thomasson
A strange bifurcation algorithm from an older iterated function system
http://youtu.be/XKhS_nklCkE
______________
// px_mutation interpolates from -4...4 across each frame; 1440 here.
_________
// angle interpolates from 0...pi2 across iterations
// px = py = 0
px = sin(angle * px_mutation);
py = cos(angle * py);
______________
Anybody should be able to reproduce it on their end. Right?
It's all 2d, but has a 3d vibe! Nice.
Any thoughts?

Maybe add audio?

[Chris M. Thomasson]

Post by sobriquet

Post by Chris M. Thomasson
A strange bifurcation algorithm from an older iterated function system
http://youtu.be/XKhS_nklCkE
______________
// px_mutation interpolates from -4...4 across each frame; 1440 here.
_________
// angle interpolates from 0...pi2 across iterations
// px = py = 0
px = sin(angle * px_mutation);
py = cos(angle * py);
______________
Anybody should be able to reproduce it on their end. Right?
It's all 2d, but has a 3d vibe! Nice.
Any thoughts?

Maybe add audio?
http://youtu.be/-T1tMQaZCtw

Oh, that would be interesting. Humm... I have some older wave code of
mine along with MIDI. Ummm. Well, I get nervous when I mess around with
my wav code because it can destroy speakers and/or eardrums! Fwiw, here
is some of my music, there is one of wavs in there. Can you find where
it starts?

There is one wav form, all the rest is MIDI. :^)

[Chris M. Thomasson]

Post by Chris M. Thomasson

Post by sobriquet

Post by Chris M. Thomasson
A strange bifurcation algorithm from an older iterated function
http://youtu.be/XKhS_nklCkE
______________
// px_mutation interpolates from -4...4 across each frame; 1440 here.
_________
// angle interpolates from 0...pi2 across iterations
// px = py = 0
px = sin(angle * px_mutation);
py = cos(angle * py);
______________
Anybody should be able to reproduce it on their end. Right?
It's all 2d, but has a 3d vibe! Nice.
Any thoughts?

Maybe add audio?
http://youtu.be/-T1tMQaZCtw

Oh, that would be interesting. Humm... I have some older wave code of
mine along with MIDI. Ummm. Well, I get nervous when I mess around with
my wav code because it can destroy speakers and/or eardrums! Fwiw, here
is some of my music, there is one of wavs in there. Can you find where
it starts?
http://youtu.be/DrPp6xfLe4Q
There is one wav form, all the rest is MIDI. :^)

Since my IFS parametric Bifurcation Diagram is already using waves,
well, it might be a perfect fir for my wave program. I just do not want
to cause any harm to speaks and/or myself. I could even use stereo with
left speaker say, sin and right speaker cos. Humm...

[Chris M. Thomasson]

Post by sobriquet

Post by Chris M. Thomasson
A strange bifurcation algorithm from an older iterated function system
http://youtu.be/XKhS_nklCkE
______________
// px_mutation interpolates from -4...4 across each frame; 1440 here.
_________
// angle interpolates from 0...pi2 across iterations
// px = py = 0
px = sin(angle * px_mutation);
py = cos(angle * py);
______________
Anybody should be able to reproduce it on their end. Right?
It's all 2d, but has a 3d vibe! Nice.
Any thoughts?

Maybe add audio?
http://youtu.be/-T1tMQaZCtw

Kind of creepy:

[Chris M. Thomasson]

Post by sobriquet

Post by Chris M. Thomasson
A strange bifurcation algorithm from an older iterated function system
http://youtu.be/XKhS_nklCkE
______________
// px_mutation interpolates from -4...4 across each frame; 1440 here.
_________
// angle interpolates from 0...pi2 across iterations
// px = py = 0
px = sin(angle * px_mutation);
py = cos(angle * py);
______________
Anybody should be able to reproduce it on their end. Right?
It's all 2d, but has a 3d vibe! Nice.
Any thoughts?

Maybe add audio?
http://youtu.be/-T1tMQaZCtw

I need to start building some wave samples. Say, for fun just
experimenting take 60 frames and use its results from my IFS as a little
sample. I would have to decide on the hertz.

[Phil Carmody]

Post by sobriquet

Post by Chris M. Thomasson
A strange bifurcation algorithm from an older iterated function
http://youtu.be/XKhS_nklCkE

Maybe add audio?
http://youtu.be/-T1tMQaZCtw

That is one of the most superb uses of sonification I have ever seen.
Hats off to you, sir.

Phil

[Chris M. Thomasson]

Post by Phil Carmody

Post by sobriquet

Post by Chris M. Thomasson
A strange bifurcation algorithm from an older iterated function
http://youtu.be/XKhS_nklCkE

Maybe add audio?
http://youtu.be/-T1tMQaZCtw

That is one of the most superb uses of sonification I have ever seen.
Hats off to you, sir.

Ditto!

[Volney]

Post by Chris M. Thomasson
A strange bifurcation algorithm from an older iterated function system
http://youtu.be/XKhS_nklCkE
______________
// px_mutation interpolates from -4...4 across each frame; 1440 here.
_________
// angle interpolates from 0...pi2 across iterations
// px = py = 0
px = sin(angle * px_mutation);
py = cos(angle * py);
______________
Anybody should be able to reproduce it on their end. Right?
It's all 2d, but has a 3d vibe! Nice.
Any thoughts?

It looks like a fractal version of an optical illusion of whether a
cylinder (with the fractal on it) is rotating in one direction or the other.

[Chris M. Thomasson]

Post by Volney

Post by Chris M. Thomasson
A strange bifurcation algorithm from an older iterated function system
http://youtu.be/XKhS_nklCkE
______________
// px_mutation interpolates from -4...4 across each frame; 1440 here.
_________
// angle interpolates from 0...pi2 across iterations
// px = py = 0
px = sin(angle * px_mutation);
py = cos(angle * py);
______________
Anybody should be able to reproduce it on their end. Right?
It's all 2d, but has a 3d vibe! Nice.
Any thoughts?

It looks like a fractal version of an optical illusion of whether a
cylinder (with the fractal on it) is rotating in one direction or the other.

Notice the alpha blend where we can see through the illusion of a 2d
plane looking 3d even with a completely 2d IFS? I did some simple 3d
volumetric protrusions of it. Well, it looks like some sort of strange
helix curve. px_mutation going from -4...4 across the frames (1440) here
is the main animation driver, so to speak. when px_mutation hits zero,
the plane is on edge where we can see a thin vertical line. In the
volumetric we can see how its a plane because we can move the camera
around it. You can see this moment right around this time:

http://youtu.be/XKhS_nklCkE

[Shayne Tai Kwan]

Post by Chris M. Thomasson

Post by Volney
It looks like a fractal version of an optical illusion of whether a
cylinder (with the fractal on it) is rotating in one direction or the other.

Notice the alpha blend where we can see through the illusion of a 2d
plane looking 3d even with a completely 2d IFS? I did some simple 3d
volumetric protrusions of it. Well, it looks like some sort of strange
helix curve. px_mutation going from -4...4 across the frames (1440) here
is the main animation driver, so to speak. when px_mutation hits zero,
the plane is on edge where we can see a thin vertical line. In the
volumetric we can see how its a plane because we can move the camera
http://youtu.be/XKhS_nklCkE

so you are scratching the shit out, you don't know what you do, and expect
magic. "it looks like a cylinder" lol.

‘𝗢𝗱𝗲𝘀𝘀𝗮_𝘄𝗶𝗹𝗹_𝗳𝗮𝗹𝗹’,_𝗠𝘂𝘀𝗸_𝘄𝗮𝗿𝗻𝘀_𝗨𝗸𝗿𝗮𝗶𝗻𝗲
Kiev should pursue a “negotiated settlement” with Moscow before it loses
all access to the Black Sea, the billionaire has argued
https://www.%72t.com/news/595173-musk-odessa-ukraine-warning/

Musk = CIA = Message to Z. Surrender.

𝗥𝘂𝘀𝘀𝗶𝗮_𝗱𝗲𝘀𝘁𝗿𝗼𝘆𝘀_𝘁𝗵𝗿𝗲𝗲_𝗨𝗸𝗿𝗮𝗶𝗻𝗶𝗮𝗻_𝘄𝗮𝗿𝗽𝗹𝗮𝗻𝗲𝘀_-_𝗠𝗼𝗗
The Russian armed forces say they targeted three Su-25s in Nikolaev
https://www.%72t.com/russia/595181-su-25-jets-nikolaev/

Happy Eoster! 👏👏👏

We want the f16 and f35! 50 years old F-16 didn't brought victory for NATO
retards in Vietnam and Afghanistan either !

the locals will be saying, the headache waiting for the Russian missiles
to arrive was getting to much.

Russian people is smashing and destroying those NATO retards ! Same as
they did in Stalingrad, Kursk, Berlin and in Vietnam !

[Chris M. Thomasson]

Post by Shayne Tai Kwan

Post by Chris M. Thomasson

Post by Volney
It looks like a fractal version of an optical illusion of whether a
cylinder (with the fractal on it) is rotating in one direction or the other.

Notice the alpha blend where we can see through the illusion of a 2d
plane looking 3d even with a completely 2d IFS? I did some simple 3d
volumetric protrusions of it. Well, it looks like some sort of strange
helix curve. px_mutation going from -4...4 across the frames (1440) here
is the main animation driver, so to speak. when px_mutation hits zero,
the plane is on edge where we can see a thin vertical line. In the
volumetric we can see how its a plane because we can move the camera
http://youtu.be/XKhS_nklCkE

so you are scratching the shit out, you don't know what you do, and expect
magic. "it looks like a cylinder" lol.

[...]

Have you tried to recreate my bifurcation diagram IFS for yourself?

[Randy Babeshko]

Post by Chris M. Thomasson

expect magic. "it looks like a cylinder" lol.

[...]
Have you tried to recreate my bifurcation diagram IFS for yourself?

what are you using for bifurcation and do you discretize, what schemes? I
guess you start with a differential math expression then discretize.

[Chris M. Thomasson]

Post by Randy Babeshko

Post by Chris M. Thomasson

expect magic. "it looks like a cylinder" lol.

[...]
Have you tried to recreate my bifurcation diagram IFS for yourself?

what are you using for bifurcation and do you discretize, what schemes? I
guess you start with a differential math expression then discretize.

I gave you the IFS I created for it:

______________
// px_mutation interpolates from -4...4 across each frame; 1440 here.

render frames:
_________
// angle interpolates from 0...pi2 across iterations
// px = py = 0

// Iteration:
px = sin(angle * px_mutation);
py = cos(angle * py);
______________

Give it a go.

[sobriquet]

Post by Chris M. Thomasson
A strange bifurcation algorithm from an older iterated function system
http://youtu.be/XKhS_nklCkE
______________
// px_mutation interpolates from -4...4 across each frame; 1440 here.
_________
// angle interpolates from 0...pi2 across iterations
// px = py = 0
px = sin(angle * px_mutation);
py = cos(angle * py);
______________
Anybody should be able to reproduce it on their end. Right?
It's all 2d, but has a 3d vibe! Nice.
Any thoughts?

I hope I can find a more suitable way to plot a bifurcation
diagram parametrically in desmos...

https://www.desmos.com/calculator/js1vnbbjjb

[Chris M. Thomasson]

Post by sobriquet

Post by Chris M. Thomasson
A strange bifurcation algorithm from an older iterated function system
http://youtu.be/XKhS_nklCkE
______________
// px_mutation interpolates from -4...4 across each frame; 1440 here.
_________
// angle interpolates from 0...pi2 across iterations
// px = py = 0
px = sin(angle * px_mutation);
py = cos(angle * py);
______________
Anybody should be able to reproduce it on their end. Right?
It's all 2d, but has a 3d vibe! Nice.
Any thoughts?

I hope I can find a more suitable way to plot a bifurcation
diagram parametrically in desmos...
https://www.desmos.com/calculator/js1vnbbjjb

Actually my parametric IFS is a parametric bifurcation diagram. The hot
spots plotted during iteration shows things off quite well. Think of
adding a little bit of color to each point that is visited during
iteration. The points with the highest colors is the main bifurcation plot.