Set of x,y,z equations similar to Lorenz?

[PDN777]

Hi,

I'm looking for other x,y,z equations similar to the Lorenz Attractor.

When I say similar, I mean this:  as the Lorenz equations generate their points, iteration after iteration, if you
plot the points in sequence, it is as if you are drawing the shape with a pencil.  The points are generated
"in order."

I am looking for other sets of fractal x,y,z equations which behave in a similar way, and produce
cool images.

Links to the equations, and perhaps animations of the sets being drawn, much appreciated.

Thanks!

--Prahas

[lkmitch]

See the listing of maps/systems of equations in this article:

https://en.wikipedia.org/wiki/List_of_chaotic_maps

[PDN777]

Thanks -- I actually found the wiki link since I posted here...

I'm working with Rossler, Rabinovich-Fabrikant, and the double pendulum.

When I say "working" -- for an eg of the fractal music I'm making -- go here:
<a href="https://www.youtube.com/v/gWkFnPHbHok&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/gWkFnPHbHok&rel=1&fs=1&hd=1</a>

FYI -- I stumbled on an interesting tool here for optimizing initial conditions:

http://demonstrations.wolfram.com/RabinovichFabrikantEquations/

Thanks!   

[claude]

I did something once with some equations I found that model a dripping tap - it's kind of nice for music because it bridges the gap between continuous differential equations (incoming flow surface tension springiness) and discrete dynamics (individual drips).  Whether my sonification is interesting is another matter, I'd recommend listening to the second version first (which is still quite long at 12mins or so...) and paying attention to the shifting rhythms (because not much else changes, it's quite a minimal drone - I should do a new version that sonifies the continuous part too).

http://mathr.co.uk/blog/2013-12-11_drip_versions.html

[PDN777]

Hi claude -- I'd like to download, but what is a .flac file?  Will Quicktime play it? 

Did you write the poem? 

Thanks for sharing.

--Prahas

[claude]

FLAC is free lossless audio codec, don't know about Quicktime support - but there's smaller to download MP3 and Ogg Vorbis versions on the archive.org page (which is linked by the picture in the blog post, not very clearly (sorry)...):
https://archive.org/details/drip-versions
there's also a streaming player on that page using HTML5 (default) or Flash
and yes, I wrote the poem too.

I watched your video, quite relaxing.  Couldn't work out the connection between visual and sound (which is probably good - I tend to have too much literal translation in my own stuff).

[PDN777]

I'll try other page later.

Re mine:  thanks for watching.  The first segment uses x,y,z data from the Lorenz system of equations to strictly create micro-musical elements: the woosh sounds. The second segment uses y data mapped to the piano melody - again a strict use of the numbers. In the third segment I write free counterpoint to accompany the y-data-generated melody. In the last segment I break free from the data and have fun! Enjoy!

[PDN777]

I like drip-version two -- I like the way the sound goes in and out of phase -- just listened to first 30 seconds -- more later.  Thanks!