a tool to build videos out of scientific calculations
besssugobesssugo is a free computational tool specifically designed to aid a cognizant expert—i.e. you, whether an engineer, scientist, technician, geek, etc—to build videos showing the result of a certain scientific calculation or whatever data can be computed or storied in a digital computer. Technically speaking, it is a plugin for the computational tool wasora, which provides means to parse and understand a high-level plain-text input file containing algebraic expressions, data for function interpolation, differential equations and output instructions amongst other facilities. Therefore, any mathematical computation which can be done by wasora—i.e. solving systems of differential-algebraic equations, multidimensional interpolation of scattered data, numerical integration and differentiation, etc.—can be combined with the facilities that besssugo provides to create visual representations in the form of animations.
Last modification: Sat, 12 Apr 2014 16:27:03 -0400.
The recommended way to get besssugo is to download the latest (0.3.7) source tarball and compile besssugo from scratch:
It should be noted that besssugo includes into its sources code from SDL2_gfx and SDL2_image, both released under the zlib license, which is GPL-compatible, so there is no need to explicitly install these libraries. However, the latter further depends optionally on libpng and libjpeg, which are needed to load images from within besssugo. Again, they can be installed with apt:
$ apt-get install libsdl2-dev
Other non-standard libraries such as SUNDIALS or Readline are optional. See both the projects wasora and besssugo relies on.
$ apt-get install libpng12-dev libjpeg8-dev
bazaar repositoryIf you plan to contribute to besssugo, modify its sources or just want to get updated versions easily, you will need to branch the development tree of besssugo, which is hosted at Launchpad using bazaar as a control revision tool. The besssugo tree can be browsed online or branched into a local copy with
If you use bzr to get the development version, you will need automake, autoconf, libtool and GNU m4. See details in the README.dev.txt file. Regular users just downloading the tarballs listed above will not need such advanced tools. Feel free to ask whatever question you may have in the mailing list.
$ bzr branch lp:besssugo
First, download the source code, uncompress, configure, make, check, install and go to examples directory:
See the documentation for detailed installation instructions.
$ wget http://www.talador.com.ar/jeremy/wasora/downloads/besssugo-0.3.7.tar.gz $ tar xvzf besssugo-0.3.7.tar.gz $ cd besssugo-0.3.7 $ ./configure $ make $ make check $ sudo make install $
the yellow bouncing ballThe first problem solved in the make check step is a yellow ball that travels from left to right bouncing at the floor over a purple background that slighly changes over time. The time of the video, the canvas size, the ball radius and the enery-loss coefficient are chosen at random:
CONST end_time w h b r c end_time = random_gauss(4,1) realtime_scale = 1 dt = 1/32 w = random_gauss(480,60) h = random_gauss(360,40) b = random(2,4) r = random_gauss(0.05,0.02) c = random(0.5,1.5) WINDOW WIDTH w HEIGHT h CAPTION "the yellow bouncing ball"\ COORDINATES 0 h w -h w HARDWARE \ COLOR 0.5+0.1*sin(2.123*t+1) 0.25+0.15*sin(1.321*t+2) 0.8+0.1*sin(1.707*t+3) x = t/end_time y = abs(cos(x*b*pi)) * exp(-c*x) CIRCLE R r X x Y y COLOR yellow BESSSUGO_DRAW
Actually, this input shows the bouncing ball on the screen. Nevertheless, the following input (which is also included in the test suite) generates a video output by first dumping the frames to individual PNG images and then using avconv to create a WebM video. The FPS are chosen at the commandline:
INCLUDE ball.was dt = 1/$1 realtime_scale = 0 OUTPUT_FILE frame ball-%04g.png step_transient BESSSUGO_DUMP FILE frame IF done PRINT "encoding video..." NONEWLINE SHELL "avconv -y -f image2 -framerate $1 -i ball-%%04d.png -vcodec libvpx ball.webm -v quiet" PRINT "ok!" PRINT "removing temporary frames..." NONEWLINE SHELL "rm -f ball-*.png" PRINT "ok!" ENDIF
find the green spotThe next tiny input generates an optical illusion. Can you find where the green spot is defined?
NUMBER n = 12 R = 0.45 r = 0.05 T = 1.25 dt = 0.5*T/n end_time = 10*T realtime_scale = 1 WINDOW WIDTH 1440 HEIGHT 920 COLOR grey50 \ CAPTION "find the green spot" CIRCLE ARRAY n X R*cos(2*pi*i/n) \ Y R*sin(2*pi*i/n) \ R r*(mod(t+(i-1)*T/n,T)>T/n) \ COLOR magenta BESSSUGO_DRAW
Again, besssugo uses the actual screen to output the trick. However, here is an scaled video of the output:
the lorenz systemBuild your own version of the Lorenz attractor by first stating which variables belong to the phase space, setting the integration time, defining the constant parameters and the initial conditions. Instead of writing the output to a text file (as in wasora's quickstart), now send the results online to the screen:
# the contents of these file between the dashed lines is # exactly equal to wasora's example file lorenz.was # -----8<--------- cut here -----8<--------- # lorenz' seminal dynamical system PHASE_SPACE x y z end_time = 40 CONST sigma r b sigma = 10 # parameters r = 28 b = 8/3 x_0 = -11 # initial conditions y_0 = -16 z_0 = 22.5 # the dynamical system x_dot .= sigma*(y - x) y_dot .= x*(r - z) - y z_dot .= x*y - b*z PRINT t x y z # -----8<--------- cut here -----8<--------- # these four lines are the ones that besssugo reads and # uses to draw a colorful representation of the # x-z phase-space plane of lorenz' butterfly # realtime_scale = 1 WINDOW WIDTH 640 HEIGHT 480 COLOR black PERSISTENT \ COORDINATES 320 480 15 -10 15 HARDWARE SEGMENT X1 last(x) X2 x Y1 last(z) Y2 z \ COLOR 0.5*(1+cos(5.071*t+1.5)) \ 0.5*(1+cos(-2.241*t+1)) \ 0.5*(1+cos(9.457*t)) BESSSUGO_DRAW
chaosStudy the chaotic nature of the Lorenz equations by slighly perturbing the initial conditions for one hundred of systems:
# this example illustrates the sensitivity to initial conditions # of the lorenz system by solving one hundred systems with # slightly different initial conditions NUMBER N 100 VECTOR vx SIZE N VECTOR vy SIZE N VECTOR vz SIZE N PHASE_SPACE vx vy vz end_time = 40 # same parameters for all cases CONST sigma r b sigma = 10 r = 28 b = 8/3 # slightly different initial conditions eps = 1e-3 vx_0(i) = -11 + eps*i vy_0(i) = -16 + eps*i vz_0(i) = 22.5 + eps*i # the dynamical systems (v stands for vector) vx_dot(i) .= sigma*(vy(i) - vx(i)) vy_dot(i) .= vx(i)*(r - vz(i)) - vy(i) vz_dot(i) .= vx(i)*vy(i) - b*vz(i) # realtime_scale = 1 WINDOW WIDTH 640 HEIGHT 480 COLOR black COORDINATES 320 480 15 -10 15 HARDWARE CIRCLE ARRAY N X vx(i) Y vz(i) RAD 0.1 COLOR 1-exp(-3*i/N) sin(pi*i/N) cos(0.5*pi*i/N) BESSSUGO_DRAW
the wasora real bookThe following sections of the wasora Real Book include examples of videos generated by besssugo:
the examples subdirectoryFollowing the idea of the wasora Real Book which consists of examples of application, the besssugo source tarball includes a subdirectory called examples which contain some ready-to-use examples. They can be browsed online at the bazaar repository.
the simple pendulumFrom the Newton, Lagrange & Hamilton section of the Wasora Real Book:
the double pendulumFrom the The double pendulum section of the Wasora Real Book:
the lorenzian chaotic waterwheelFrom tge The chaotic Lorenzian waterwheel section of the Wasora Real Book:
There exist a mailing list < wasora @ talador.com.ar > where questions can be posted about any aspect of the code, including intallation, usage and development. Besides suscribing and directly asking a question, you can also browse the archives. Bugs reports are also welcome.
besssugo is free software, and as such it is developed under a free operating system, namely Debian GNU/Linux. The distribution tarball is based on GNU Autoconf & friends, so besssugo should build in any POSIX-compliant environment. However, besssugo is a fairly complex piece of software, so portability is not guaranteed (but improvements are welcome). Running besssugo in non-free operating systems is discouraged, and such topic is not of the interest of the author of besssugo. However, contributions and experiences may be well received if discussed in the mailing list.
projects besssugo relies on
optional librariesTo be done.
© jeremy theler 2004—2015