fractals in sage
William Stein
A student of mine is going to add to sage the capability of plotting
lots and lots of fractals easily. E.g.,
sage: fractals.[tab]
lots of stuff
sage: fractals.julia([params]).show(figsize=10)
[up pops a julia set]
The trac ticket where this starts is here:
http://trac.sagemath.org/sage_trac/ticket/8423
This isn't going to be some complicated fancy object oriented
abstract dynamical metaclassed framework. It's just a bunch of
functions to draw fractals. And at first it could even be slow
(though obviously some cython master will probably clear through it at
some point and make everything really fast, without having to change
or write any docs). I can imagine that most of the files will consist
of examples and docstrings rather than actual code, too.
The point of this email: if you like plotting fractals, and have some
potentially useful code to contribute, then please post to this thread
or http://trac.sagemath.org/sage_trac/ticket/8423 with them. Or if
you really want to help, then do so.
-- William
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
mhampton
I do much, although I couldn't resist adding a little to the ticket
already.
-Marshall
On Mar 2, 1:15 pm, William Stein <wst...@gmail.com> wrote:
> Hi,
>
> A student of mine is going to add to sage the capability of plotting
> lots and lots of fractals easily. E.g.,
>
> sage: fractals.[tab]
> lots of stuff
>
> sage: fractals.julia([params]).show(figsize=10)
> [up pops a julia set]
>
> The trac ticket where this starts is here:http://trac.sagemath.org/sage_trac/ticket/8423
>
> This isn't going to be some complicated fancy object oriented
> abstract dynamical metaclassed framework. It's just a bunch of
> functions to draw fractals. And at first it could even be slow
> (though obviously some cython master will probably clear through it at
> some point and make everything really fast, without having to change
> or write any docs). I can imagine that most of the files will consist
> of examples and docstrings rather than actual code, too.
>
> The point of this email: if you like plotting fractals, and have some
> potentially useful code to contribute, then please post to this thread
> orhttp://trac.sagemath.org/sage_trac/ticket/8423with them. Or if
Florent Hivert
> A student of mine is going to add to sage the capability of plotting
> lots and lots of fractals easily. E.g.,
[...]
> The point of this email: if you like plotting fractals, and have some
> potentially useful code to contribute, then please post to this thread
> or http://trac.sagemath.org/sage_trac/ticket/8423 with them. Or if
> you really want to help, then do so.
I don't remember who he was, but at the end of sage days 20, one guys made a
short demo about plotting some Rauzy fractal. I don't know the precise
definition but I think it is related to numerations systems in a non integer
base (e.g. the golden number). I cc this mail to sage-combinat-devel where
someone certainly knows the precise guy.
Cheers,
Florent
Vincent Delecroix
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>
Hi William, hi Florent,
Perhaps Timo Jolivet (I show from him nice pictures during SAGE days
20) ? We planned with him and Stepan Starosta to implement two way of
plotting Rauzy fractals in SAGE for tomorrow afternoon ! If everything
goes well, there will be a ticket ready tomorrow evening (Paris time).
I won't forget the shortcut fractals.RauzyFractal
Cheers,
Vincent
Harald Schilly
> A student of mine is going to add to sage the capability of plotting
> lots and lots of fractals easily.
That sounds exiting, are there also plans to implement "discrete"
fractals? (combinat.WordMorphisms and word-paths and things like
that?)
http://www.sagemath.org/doc/reference/sage/combinat/words/paths.html
http://alexis.monnerot-dumaine.neuf.fr/articles/fibonacci%20fractal.pdf
Disclaimer: I'm not sure if this is really related, just something I
had in the back of my head ;)
Another thing that comes to my mind are images like that one:
http://serendip.brynmawr.edu/bookshelves/NKS0032.gif
h
Dr. David Kirkby
Those sorts of images could be good for your calender.
I recall many years ago programming the 80387 maths coprocessor chip at the
assembly level to generate the fastest Mandlebrot set I could. If I recall
correctly, it ran at 25 MHz, which I think was the fastest any 80386/80376 chip
run at.
There is the open-source 'fractint' program which does the same sort of thing,
but in integer maths, which is obviously quicker, though the floating point
processors now are a lot better than they used to be. I recall computing tables
of sin() and cos() for Monte Carlo simulations, then using a lookup rather than
compute the sines and cosines each time, as it was too slow. Now, you are better
to just call sin or cos in an FPU, rather than look them up in a table.
I'm giving my age away a bit here!
Dave
William Stein
> On Mar 2, 8:15 pm, William Stein <wst...@gmail.com> wrote:
>> A student of mine is going to add to sage the capability of plotting
>> lots and lots of fractals easily.
>
> That sounds exiting, are there also plans to implement "discrete"
> fractals? (combinat.WordMorphisms and word-paths and things like
> that?)
>
> http://www.sagemath.org/doc/reference/sage/combinat/words/paths.html
> http://alexis.monnerot-dumaine.neuf.fr/articles/fibonacci%20fractal.pdf
>
> Disclaimer: I'm not sure if this is really related, just something I
> had in the back of my head ;)
Yes, sure. There really isn't so much in the way of *big plans*
here. We just want
fractals.[tab]
to be a way to draw tons of cool pictures easily. It'll be a lot of fun.
William
>
> Another thing that comes to my mind are images like that one:
> http://serendip.brynmawr.edu/bookshelves/NKS0032.gif
>
> h
>
> --
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Ondrej Certik
So how long did it take to calculate the 256x265 pixels mandelbrot
set? I remember it took couple hours for me (I wrote it in Pascal...).
>
> There is the open-source 'fractint' program which does the same sort of
> thing, but in integer maths, which is obviously quicker, though the floating
> point processors now are a lot better than they used to be. I recall
> computing tables of sin() and cos() for Monte Carlo simulations, then using
> a lookup rather than compute the sines and cosines each time, as it was too
> slow. Now, you are better to just call sin or cos in an FPU, rather than
> look them up in a table.
Right.
Ondrej
Florent Hivert
> I recall many years ago programming the 80387 maths coprocessor chip at the
> assembly level to generate the fastest Mandlebrot set I could. If I recall
> correctly, it ran at 25 MHz, which I think was the fastest any 80386/80376
> chip run at.
Wow ! Advanced technology ! I recall doing it on an Apple II, 6502 1Mhz ;-)
Cheers,
Florent
slabbe
> > fractals? (combinat.WordMorphisms and word-paths and things like
> > that?)
>
> >http://www.sagemath.org/doc/reference/sage/combinat/words/paths.html
> >http://alexis.monnerot-dumaine.neuf.fr/articles/fibonacci%20fractal.pdf
I just added on the animate page of the sage wiki an animation [1]
that was dying in one of my folder. A fractal sequence of tiles
related to the Fibonacci sequence. Maybe sage: fractals.fibonacci_tile
could exist and return a .png file? or maybe a tikzpicture? One can
obtain the tikz code in two lines :
sage: w = words.fibonacci_tile(2)
sage: w.tikz_trajectory()
'(0, 0) -- (0, -1) -- (-1, -1) -- (-1, -2) -- (0, -2) -- (0, -3) --
(1, -3) -- (1, -2) -- (2, -2) -- (2, -3) -- (3, -3) -- (3, -4) -- (2,
-4) -- (2, -5) -- (1, -5) -- (1, -4) -- (0, -4) -- (0, -5) -- (-1, -5)
-- (-1, -6) -- (0, -6) -- (0, -7) -- (-1, -7) -- (-1, -8) -- (-2, -8)
-- (-2, -7) -- (-3, -7) -- (-3, -6) -- (-2, -6) -- (-2, -5) -- (-3,
-5) -- (-3, -4) -- (-4, -4) -- (-4, -5) -- (-5, -5) -- (-5, -4) --
(-6, -4) -- (-6, -3) -- (-5, -3) -- (-5, -2) -- (-4, -2) -- (-4, -3)
-- (-3, -3) -- (-3, -2) -- (-2, -2) -- (-2, -1) -- (-3, -1) -- (-3, 0)
-- (-2, 0) -- (-2, 1) -- (-1, 1) -- (-1, 0) -- (0, 0)'
I think the idea of having fractals.[TAB] is great.
Sébastien
slabbe
> > fractals? (combinat.WordMorphisms and word-paths and things like
> > that?)
>
> >http://www.sagemath.org/doc/reference/sage/combinat/words/paths.html
> >http://alexis.monnerot-dumaine.neuf.fr/articles/fibonacci%20fractal.pdf
I just added on the animate page of the sage wiki an animation [1]