SCARAB
------
A Lorenz attractor numerical integrator.
Written by Alberto Menegazzi from Milano, Italy.
e-mail: flash.egon@iol.it


THE PROGRAM PURPOSE
-------------------
Scarab's purpose is to :
	
	* calculate the solution of the Lorenz attractor differential
	  system using diffent methods.

	* plot or save to a file the solution.


THE USER CHOICES
----------------
In this version the user has full control over:

	* coefficients delta, b and r of the differential system.

	* point where the integration will start (initial conditions).

	* lenght of the range of integration.


THE COMMAND LINE
----------------
SCARAB  [-e] [-k] [-d n] [-b n] [-r n] [-x n] [-y n] [-z n]
	[-t n] [-h]

-e   : use forward Eulero method (default)
-k   : use Runge-Kutta 4-th order method (not avaible!)
-d n : change delta coefficient (default 10)
-r n : change r coefficient     (default 28)
-b n : change b coefficient     (default 8/3)
-x n : change the starting conditions, x coord (default 1)
-y n : change the starting conditions, y coord (default 1)
-z n : change the starting conditions, z coord (default 1)
-t n : change the range of integration         (default 10)
-h   : print this help


THE LORENZ ATTRACTOR
--------------------
The Lorenz attractor is meterologic model developed by prof. Lorenz 
of MIT in 1963 and it's a three equation differential system that 
comes from the truncation after few terms of the Couette flow.
The x stands for the length of the convective flow, the y for the 
difference of temperature between two flows side by side and the z
for the linear deviation of temperature from a linear profile.


WHO AM I ? (who cares ?)
------------------------
I'm a student of aeronautic engeenering in Milan and I'm interested in
this problem not for it's direct result, but to experiment some
knowledges after a numerical calculus exam and also because I've
been affacinated by the beautiness of the graphical result.


WHAT CAN THE PROGRAM DO AT THIS TIME ?
--------------------------------------
The only method implemented in this version is an easy forward Eulero method
time step fixed, just to test the inteface of my program with Gnuplot.
As it's the first time I write code for Unix (I'm a second-rate C dos
programmer), I would appreciate a lot some help from the testers of the code.


WHAT DO I WHAT TO DEVELOPE ?
----------------------------
Look in the TODO file.


WHAT DO I NEED ?
----------------
First of all a grammar correction to this README file and the TODO file,
than suggestions about new methods and new ideas what you would like to see
in future releases.

My biggest problem stands in the plot of the solution. Current version of Scarab
writes two temporary files, one with some commands for Gnuplot as if they were
given by the user (set param, splot "<tempfilename>" with lines, pause -1), and
the other file contains the coords of the points to be plotted in the format
needed by Gnuplot after setting param. Than Scarab executes Gnuplot with
"system", passing together the name of the file that holds the commands and than
Gnuplot loads the coords of the points from the other file and plots them
waiting the user to press enter. 
I now have some questions :
	* Do you have any different idea for plotting the solution ? 
	* Can I launch Gnuplot and control it by the pipe command ?
	  It would be useful as I could change the viewpoint directly from
	  Scarab.
	* Is it difficult to write an own function to plot the solution ?
	  What kind of library would you suggest me ? Xforms, Tcl/TK, ... ?
	  Are they easy to learn ? And what's an easy solution for a
	  graphic user interface between these libs ?

How can I write a decent Makefile? (The one that comes with Scarab is caught
from another program and modified with a bit of luck).
Where is possible to find electronic docs about how to write makefiles?

Would be necessary to translate in english my comments /* blah blah */ along
the .c an .h files ?

Is is difficult to launch and drive new tasks from the program? I'm now
thinking about a task that plots the solution as points are calculated.

BUGS, HELP AND INFO
-------------------
MY E-MAIL : flash.egon@iol.it
Feel free to write me any suggestion or if any bug is present, but PLEASE let
me know if you think my program is interesting.
