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<DIV><FONT face=Arial size=2>Hi ..still on the topic of Lorenz attarctors and
chaos..it might be fun to see if one could design an anlogue circuit
that solves the so called' logistic equation'</FONT></DIV>
<DIV><FONT face=Arial size=2>(for those who like maths see </FONT><FONT
face=Arial size=2><A
href="http://mathworld.wolfram.com/LogisticEquation.html">http://mathworld.wolfram.com/LogisticEquation.html</A> for
a nice review and pretty pictures) . The solutions to this equation (or at least
the recurrence relation thats based on this equation) can approach chaos
..and show period doubling and bifurcation etc. I would guess it must
be possible to solve simple recurrence relations using analogue computer type
circuits?</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>cheers</FONT></DIV>
<DIV><FONT face=Arial size=2>steve thomas</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<BLOCKQUOTE dir=ltr
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B>
<A title=aon.912230836@aon.at href="mailto:aon.912230836@aon.at">Jaroslaw
Ziembicki</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=synth-diy@dropmix.xs4all.nl
href="mailto:synth-diy@dropmix.xs4all.nl">SDIY</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Friday, July 04, 2003 11:07
AM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> [sdiy] Digital simulation of the
Lorenz attractor</DIV>
<DIV><BR></DIV>
<DIV><FONT face=Arial size=2>Hi,</FONT></DIV>
<DIV><FONT face=Arial size=2>I wrote a C program that simulates the
Lorenz attractor</FONT></DIV>
<DIV><FONT face=Arial size=2>and plots the results. The graphic mode
should be set.</FONT></DIV>
<DIV><FONT face=Arial size=2>Here is the basic subroutine. Maybe somebody
will find</FONT></DIV>
<DIV><FONT face=Arial size=2>it useful.</FONT></DIV>
<DIV><FONT face=Arial size=2>
<DIV><FONT face=Arial size=2>Regards</FONT></DIV>
<DIV><FONT face=Arial size=2>Jarek</FONT></DIV></FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>void Lorenz(void)<BR>{<BR>/* simulation
variables/parameters: */<BR> float x = 0.1;<BR> float y
= 0.0;<BR> float z = 0.0;<BR> float s = 10.00;<BR>
float r = 28.00;<BR> float b = 2.67;<BR>
float dt = 100E-6;<BR>/* graphics' variables/parameters: */<BR>
float xxscale = 0.02*(float)(getmaxx()+1); /* for plot scaling
*/<BR> float yyscale = 0.01*(float)(getmaxy()+1); /* for plot
scaling */<BR> WORD xx0 =
(getmaxx()+1)/2; /* plot center x */<BR>
WORD yy0 = (getmaxy()+1)/2; /* plot center y
*/<BR> WORD color = 15;</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>/* border, x and y axes: */<BR>
setcolor(DARKGRAY);<BR>
rectangle(0,0,getmaxx(),getmaxy());<BR> line(0,yy0,getmaxx(),yy0);
line(xx0,0,xx0,getmaxx());<BR>/* loop: */<BR> while ( kbhit() )
getch();<BR> do<BR> {<BR>
float dx,dy,dz;<BR> WORD
xx,yy;</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2> /* put a pixel: */<BR>
xx = xx0+(int)(xxscale*x); yy = yy0-(int)(yyscale*z);<BR>
putpixel(xx,yy,color);<BR> /* new x,y,z values:
*/<BR> dx = dt * (s*(y-x));<BR> dy = dt *
(r*x - y - x*z);<BR> dz = dt * (x*y -
b*z);<BR> x += dx; y += dy; z += dz;<BR>
/* next color: */<BR> color++; if ( color >
15 ) color = 0;<BR> }<BR> while ( !kbhit() );<BR>}</FONT></DIV>
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