English
资源说明：Chaos calculates the predictability of a very simple physical system in very high precision and is able to write the results to a TIFF file.
Chaos 0.9 ========= This program was written by Mathijs de Bruin as an exercise during a course in numerical physics at the University of Amsterdam in 2006. It is a GPL'd program that calculates the predictability of a very simple physical system in very high precision and is able to write the results to a TIFF file. The program is available at: http://www.dokterbob.net/files/chaos/ What it does ============ This program does calculations on a fairly simple physical system, namely a spring pendulum: consider a nail in a wall with a spring dingling on it with a weight connected to it. The motion of this system can be described by two very simple differential equations, if the both the gravitational constant, the spring constant and the mass of the weight are taken to equal one. xdotdot = x*(1 - sqrt(x^2+y^2))/sqrt(x^2+y^2) ydotdot = y*(1 - sqrt(x^2+y^2))/sqrt(x^2+y^2) - 1 Using these equations I can numerically calculate the position after a certain time given a initial speed and position are known. What I do here to acquire a brightness value for each pixel is solving these equations four times for each pixel. First I calculate the position at a specified time with a starting position just left of the 'center' of the pixel. Then I go and do the same to the right of this pixel. Of these two positions I take the absolute value of the difference of the horizontal component. The same goes for the vertical component; I calculate a little above the pixel and a little bit under it and take the distance between them in the vertical direction. These two values are added to yield for each pixel a floating point value which is then nor- malized and written to a TIFF file. After that the time is increased (or actually, the calculations are _continued_, the program keeping in memory the place it stopped calculating) so we can actually _see_ 'chaos' emerging. For Dutch speakers, more information can be found at my website, where I have the ancestor of this program implemented in Mathematica: http://files.dokterbob.net/mathematica-project/ Requirements ============ - The program makes use of libtiff, which is freely available at http://www.remotesensing.org/libtiff/ - Furthermore I use a library called daa written by Richard A. Hogaboom to efficiently allocate multi-dimensional arrays which is a little less freely available at his website http://www.embedded.com/2000/0012/0012feat4.htm This library is, for now, included but I am not sure as to whether this is copyright in- fringement so we'll see... - The GNU getopt, part of the GNU C library. If not part of your system you might want to try freegetopt, found at http://freegetopt.sourceforge.net/ - ImageMagick if you plan on using some of the flashy tricks denoted hereunder. See: http://www.imagemagick.org/ Compiling ========= Compiling the program is fairly simple. One is able to specify the CPU type as understood by the gcc -march=parameter, so for a Pentium 4 this would be CPU=pentium4. This program relies very heavy on compiler optimization so you'd better get this right. SSE2=1 lets make know you've got SSE2 available and want to use it, same goes for the LZW parameter. A lot of older versions of libtiff don't have LZW-compression enabled because of now-expired patents. With the parameter FINISH=1 one can enable automatic 2x anti-aliasing, contrast optimization and BMP-conversion using ImageMagick, given that you have that program installed at all. make CPU= SSE2=1 LZW=1 After compiling the program automatically starts calculating with the default values. How to use ========== The usage of this program is about as simple as the compilation. Compiled-in default parameters can be changed in params.h. Most of them can be tuned at the command line thru the following parameters: --xmin Floating point denoting the leftmost part of the calculated interval --xmax If xmin + xmax = 0 the program calculates twice as fast because of the symmetry of the results. Recommended! --ymin The y interval. Ain't no symmetry here dude. --ymax --tstep Increase of time after each image has been written. --tmax Amount of time after which to buzz off. If negative the program will calculate until infinity. --steps The amount of steps per time unit, so steps=1000 and tstep=0.1 yields 100 steps per written image. By default TIFF images are written in the img/ directory numbering from 00000 to 99999. Please mail me when you get there! ;) Contact ======= If you specifically (don't) like this program, have extended it or just plainly have created beutiful pictures with it please don't hesitate to let me know. Mail me at drbob@dokterbob.net.
本源码包内暂不包含可直接显示的源代码文件，请下载源码包。
