Below you will find pages that utilize the taxonomy term “Fractals”
You know how you slip once on a habit and everything goes crazy? Well, I’ve been 4 weeks without writing these, so here’s the accumulated reading from 4 weeks. Because, even if I don’t write it, I read a lot anyway. Also, there’s lot of interesting content this “week”.
I had always wanted to play with Processing (after leafing through The
Processing
Handbook and
Visualizing
Data
some years ago). My general dislike for Java or the JVM made me just play a
short amount of time with processing.js something around 2011 (there was a
native processing.js application for iOS, I used it for a while on my iPad and
iPod Touch).
A few weeks ago I started trying a pre-beta release of Dyalog APL (now available as “full beta”) for Mac. Fellow Mac users, looks like we are in for a treat after so much time of only having GNU APL and the pretty expensive APLX. Now Mac APL lovers, users and aficionados will have a competitive, commercial option. At last!
I started with the usual 1+1, ⍳ 10 , ⍴ ⍳ 10 to check it worked as expected.
Is this line noise?
⍉' *'[⍎'1+0<|z',(∊150⍴⊂'←c+m×m'),'←c←(¯2.1J¯1.3+(((2.6÷b-1)×(¯1+⍳b))∘.+(0J1×(2.6÷b-1)×(¯1+⍳b←51))))'] Nope. This is not line noise, but a complete APL program to display the Mandelbrot set in glorious ASCII, with asterisks and spaces just like Brooks and Matelski did a long time ago while studying Kleinian groups (it’s a short paper, read it someday). I’ll explain in (a lot, I hope) detail this line in a few moments. So, what’s APL first?
This was computed using PVM and the full PDF generated is 16k pixels wide
Today is Iceland’s National Day (commemorating their independence day and the date of birth of Jón Sigurðsson), and to commemorate it I share this image with everyone.
I computed this image a long, long time ago (using the Distance Estimator Method, paralellised with PVM using 16 computers, it took just 2 minutes). The full file is a 30MB pdf, which I printed large-size (2 meters wide), and sits in my office.
A week without writing here. A week with little thesis related work done. But it has also been a week with ideas and things and such. You know, two weeks ago I was in Dresden for a conference. Lots of parallel sessions, and quite a few time to think. This post is mostly a digest from my life bookmarks for these two weeks.
Several complex dynamic ideas: Unrelated to my thesis, but I’ve been thinking about them these days.
As you may remember, I spent quite some time this August with Lavaurs algorithm for the topological identification of the circle corresponding to the Mandelbrot set. After that, I spent quite some more trying to do pictures of external rays to show side by side. I was not able… and then found Mandel.
Thanks to Mandel, LISP and my Lavaurs code
Really nice program, with lots and lots of options (and I met the programmer, which happens to be also mathematician, we met at a conference).
As you may already know, I presented a poster at a conference recently, and did the set up with Scribus, the texts with LaTeX with the Beamer and Beamerposter packages.
Setting up
Note from 2019: I can’t find the final version of that poster, only a modified version from a few months later for another conference.
The first piece of advise, is to set page guides where needed (in the Page menu, you can put them at a certain numerical place, and then move them along) and then Snap to guides in the same menu.
Just 5 excerpts of it
Related posts:
And “e” appears from nowhere!9 programming books I have read and somewhat liked…
C code juicer: detecting copied programming assignments
Cron, diff & wget: Watch changes in a webpage
8 reasons for re-inventing the wheel as a programmer
Approximating images with randomly placed translucent triangles
ParseList(ScrambleList(Relateds(Linux, Programming)),10)
From flickr
September is to months as Monday is to weekdays
September is again here, like a new year in more than a sense. I have no new “New Year’s promises”, since the beginning of the year. In fact, most of the things I wanted to do are already done, on the way to be done or I gave up. Well, let’s summarize what I shall do these three months to end 2009
These days I’ve been busy programming a version of Lavaurs algorithm for the idenfication of circle chords: the abstract Mandelbrot set.
The images don’t look like much, but the output of the program is nicer: it outputs an Encapsulated PostScript file which looks sharper. But when converting to png with ImageMagick some distortion appeared.
Lavaurs chords, depth 13 cutoff
Lavaurs chords, depth 5
Lavaurs chords, depth 13
Lavaurs algorithm on course
Like almost every year, August comes with a lot of pending To Do lists… This year, it is choking full, mostly of work related issues, and some unknotted threads waiting to be finished. And in two and a half weeks I’ll head for Paris, and then my “vacation” is over.
Yesterday I wasted my morning: bought my orange belt, set up the external monitor for my netbook, configured the printer, fotocopied two pages of a book and drank an horchata with a friend.
As I already did with Douady Rabbits, here is another dynamical plane, this time corresponding to a Siegel disk in an entire transcendental family in a parameter corresponding to a polynomial-like region.
Siegel disk in an ETF, available below as wallpaper
Siegel disk for desktop background 1280x800
Siegel disk for desktop background 1024x768
You can also buy a poster version here.
If you liked it, or have whatever else to say please leave a comment, digg, stumble or whatever you feel like doing.
I have been experimenting with exponential-power potentials in my fractal images as of late, and by far the best results have been these. You can download it as a desktop wallpaper, hope you enjoy it. This Douady rabbit appears as a capture zone for a critical value in an exponential family.
Douady rabbit in an exponential family, available below as wallpaper
Douady rabbit for desktop background 1280x800
Douady rabbit for desktop background 1024x768