[genius] Fri Dec 16 17:36:16 2016 Jiri (George) Lebl <jirka 5z com>

[George Lebl <jirka src gnome org>]

commit ce147f2a094d6eab03184edbdf2fe9e9774b9c7e
Author: Jiri (George) Lebl <jiri lebl gmail com>
Date:   Fri Dec 16 17:36:33 2016 -0600

    Fri Dec 16 17:36:16 2016  Jiri (George) Lebl <jirka 5z com>
    
        * examples/complex-analysis-argument-principle.gel: Add argument
          principle example
    
        * examples/complex-analysis-mandelbrot-set.gel: slightly modify, try
          more iterations

 ChangeLog                                        |    8 ++
 examples/Makefile.am                             |    1 +
 examples/complex-analysis-argument-principle.gel |  103 ++++++++++++++++++++++
 examples/complex-analysis-mandelbrot-set.gel     |   14 ++--
 4 files changed, 119 insertions(+), 7 deletions(-)
---
diff --git a/ChangeLog b/ChangeLog
index e66aa9b..c63e5f1 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,11 @@
+Fri Dec 16 17:36:16 2016  Jiri (George) Lebl <jirka 5z com>
+
+       * examples/complex-analysis-argument-principle.gel: Add argument
+         principle example
+
+       * examples/complex-analysis-mandelbrot-set.gel: slightly modify, try
+         more iterations
+
 Tue Nov 22 14:51:35 2016  Jiri (George) Lebl <jirka 5z com>
 
        * src/funclib.c: fix doc string for ErrorFunction,  Thanks to
diff --git a/examples/Makefile.am b/examples/Makefile.am
index ff7518e..df2f16f 100644
--- a/examples/Makefile.am
+++ b/examples/Makefile.am
@@ -28,6 +28,7 @@ example_DATA = \
        complex-analysis-mandelbrot-define.gel \
        complex-analysis-wandering-ball.gel \
        complex-analysis-mesh.gel \
+       complex-analysis-argument-principle.gel \
        riemann-integral.gel \
        riemann-integral-darboux.gel
 
diff --git a/examples/complex-analysis-argument-principle.gel 
b/examples/complex-analysis-argument-principle.gel
new file mode 100644
index 0000000..40a6ab8
--- /dev/null
+++ b/examples/complex-analysis-argument-principle.gel
@@ -0,0 +1,103 @@
+# Category: Complex Analysis
+# Name: Finding roots via argument principle
+#
+# Shows a bouncing wandering ball and prints the number of roots minus poles of
+# a function within the ball to the console.  When roots detected the ball
+# turns green, for poles, it turns red. If the mouse is within the plot window
+# then the ball will be over the mouse.
+
+
+#The function to try, (must be able to take symbolic derivative, otherwise 
+#set df below!)
+
+function f(z) = (z-5i-5)^3*(z+5i-10)/(z+5i+5);
+#function f(z) = (z-4+1i)*(z-3)*(z-5i);
+#function f(z) = sin(2*z)*(z-5i+5)*(z+5);
+#function f(z) = sin(pi*z);
+
+df = SymbolicDerivative(f);
+
+LinePlotDrawLegends = false;
+PlotWindowPresent(); # Make sure the window is raised
+LinePlotClear(); # make sure we are in the line plot mode
+
+#approximately square grid
+LinePlotWindow = [-13,13,-10,10];
+
+#confine possibly to a smaller window.
+#You can also zoom out during the animation.
+#confine_window = [-8,8,-7,7];
+confine_window = LinePlotWindow;
+
+#the circle
+radius = 3;
+step = 0.1;
+
+circlepts = ApplyOverMatrix((0:(120))',`(k)=radius*exp(k*1i*2*pi/(120)));
+
+function draw_ball(pt,N) = (
+       PlotCanvasFreeze ();
+       LinePlotClear ();
+
+       LinePlotDrawLine (pt + circlepts, "color",
+                         if N>0 then "green" else if N<0 then "red" else "blue");
+
+       PlotCanvasThaw ();
+);
+
+dir = exp(1i*rand()*2*pi);
+pt = 0;
+lastp = null;
+
+function NumberOfZeros(pt) = (
+  N = (1/(2*pi))*CompositeSimpsonsRule(`(t)=(
+    #f'(z)/f(z)
+    ( df(pt+radius*exp(1i*t)) / f(pt+radius*exp(1i*t)) ) *
+    # dz/i
+    radius*exp(1i*t)
+  ),0,2*pi,20);
+  return round(Re(N));
+);
+
+while true do (
+       p = LinePlotMouseLocation ();
+       if IsNull(p) then break;
+       
+       # if mouse within window, use that
+       if confine_window@(1) <= p@(1) <= confine_window@(2) and
+          confine_window@(3) <= p@(2) <= confine_window@(4) then (
+               pt = p@(1) + 1i*p@(2);
+               # if at the same point, then just try again;
+               if pt == lastp then (wait(0.0001);continue);
+               lastp = pt
+       );
+
+       N = NumberOfZeros(pt);
+       draw_ball(pt,N);
+       print ("Zeros-Poles within ball: " + N + "  ... may be nonsense if zero/pole on circle");
+
+       # Now wander around
+
+       pt = pt+step*dir;
+
+       if (Re(pt) < confine_window@(1)+radius) then (
+               pt = (confine_window@(1)+radius) + 1i*Im(pt);
+               dir = -1i*conj(1i*dir)
+       );
+       if (Re(pt) > confine_window@(2)-radius) then (
+               pt = (confine_window@(2)-radius) + 1i*Im(pt);
+               dir = -1i*conj(1i*dir)
+       );
+       if (Im(pt) < confine_window@(3)+radius) then (
+               pt = Re(pt) + 1i*(confine_window@(3)+radius);
+               dir = conj(dir)
+       );
+       if (Im(pt) > confine_window@(4)-radius) then (
+               pt = Re(pt) + 1i*(confine_window@(4)-radius);
+               dir = conj(dir)
+       );
+
+       dir = dir*exp(1i*(rand()*0.2-0.1));
+
+       wait(0.0001)
+);
diff --git a/examples/complex-analysis-mandelbrot-set.gel b/examples/complex-analysis-mandelbrot-set.gel
index 4517ea0..a644c65 100644
--- a/examples/complex-analysis-mandelbrot-set.gel
+++ b/examples/complex-analysis-mandelbrot-set.gel
@@ -4,7 +4,7 @@
 # Draw the Mandelbrot set
 #
 
-iterations = 10;
+iterations = 30;
 
 LinePlotWindow = [-2,2,-2,2];
 
@@ -29,13 +29,13 @@ for x = -2.0 to 2.0 by 0.02 do (
       z = z^2+c;
       if |z| >= 2.0 then break
     );
-    if m == iterations then (
+    if m == iterations then
       points = [points;c];
-      increment k;
-      # every 100 point display intermediate picture
-      if k % 100 == 0 then
-        DrawThePlot()
-    )
+    
+    increment k;
+    # every 500's point display intermediate picture
+    if k % 500 == 0 then
+      DrawThePlot()
   )
 );