(************** Content-type: application/mathematica **************
                     CreatedBy='Mathematica 5.0'

                    Mathematica-Compatible Notebook

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Notebook[{

Cell[CellGroupData[{
Cell["Exploring The Mandelbrot Set", "Title"],

Cell["\<\
The functions 
                          drawMB[xr, yr]
                          drawMBwithBox[xr, yr, xrb, yrb]
plot part of the Mandelbrot set where xr specifies the inteval on the x-axis \
and yr specifies the interval on the y-axis.  To create sequences of pictures \
where each gives a zoomed-in view of part of the previous image, use \
drawMBwithBox[xr, yr, xrb, yrb] to draw the current view with a box placed to \
show the region to be drawn at the next step. Here xrb and yrb specify \
intervals on the x and y axes defining the box.  See the examples below.
                          \
\>", "Text"],

Cell["Off[General::spell1];", "Input",
  CellOpen->False,
  InitializationCell->True],

Cell["\<\
f[x_, y_, max_] := ( z = c = x + I*y; i = 0; While[ Abs[z] < 2.0 && i < max, \
z = z*z + c; i++ ]; Return[i]; )
box[xr_,yr_]:= \
Line[{{xr[[1]],yr[[1]]},{xr[[2]],yr[[1]]},{xr[[2]],yr[[2]]},{xr[[1]],yr[[2]]},\
{xr[[1]],yr[[1]]}}];
drawMB[xr_,yr_,shw_:True]:= DensityPlot[ f[x, y, 60], Evaluate[Flatten[{x, \
xr}]], Evaluate[Flatten[{y, yr}]], PlotPoints -> 300, Mesh -> False, \
ColorFunction -> Hue, Evaluate[If[shw == \
True,DisplayFunction->$DisplayFunction,DisplayFunction->Identity]]];
drawMBwithBox[xr_,yr_,xrb_,yrb_]:= Show[drawMB[xr,yr,False], \
Graphics[box[xrb,yrb]], DisplayFunction->$DisplayFunction]\
\>", "Input",
  InitializationCell->True,
  FontFamily->"Courier New"],

Cell["drawMB[{-2.25,.75},{-1.5,1.5}];", "Input"],

Cell["drawMBwithBox[{-2.25,.75},{-1.5,1.5},{-.3,.1},{-1.2,-.7}];", "Input"],

Cell["drawMB[{-.3,.1},{-1.2,-.7}];", "Input"],

Cell["\<\
drawMBwithBox[{-.3,.1},{-1.2,-.7},{-.18,-.14},{-1.06,-1.01}];\
\>", "Input"],

Cell["drawMB[{-.18,-.14},{-1.06,-1.01}];", "Input"],

Cell["\<\
drawMBwithBox[{-.18,-.14},{-1.06,-1.01},{-.152,-.15},{-1.045,-1.042}];\
\>", "Input"],

Cell["drawMB[{-.152,-.15},{-1.045,-1.042}];", "Input"]
}, Open  ]]
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WindowSize->{1016, 651},
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]

(*******************************************************************
Cached data follows.  If you edit this Notebook file directly, not
using Mathematica, you must remove the line containing CacheID at
the top of  the file.  The cache data will then be recreated when
you save this file from within Mathematica.
*******************************************************************)

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Cell[1824, 55, 620, 11, 147, "Text"],
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  InitializationCell->True],
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Cell[3649, 104, 54, 0, 30, "Input"]
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*)



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End of Mathematica Notebook file.
*******************************************************************)