Arjen Markus (25 august 2003) I got to know them during the hype in the late 1980s: pictures of the Mandelbrot set -- beautiful, enigmatic and so easy to create!
Later, I learned their counterpart too: Julia sets. And now, more than a decade later, I have finally taken the time to do them in Tcl too.
Here is a quickly written script - I will use it in one of the chapters for the young programmers' tutorial/booklet ...
(I have not cleaned up the code and there is no GUI to select between the two types, or to change the parameters or to zoom in ...)
# Mandelbrot and Julia pictures
#
proc det_iteration { zx zy cx cy maxiter } {
set znx $zx
set zny $zy
set noiter -1
for { set i 0 } { $i < $maxiter } { incr i } {
if { hypot($znx,$zny) > 2.0 } {
set noiter $i
break
}
set znnx [expr {$znx*$znx-$zny*$zny+$cx}]
set znny [expr {2.0*$znx*$zny+$cy}]
set znx $znnx
set zny $znny
}
return $noiter
}
proc setpixel { image xpix ypix noiter } {
if { $noiter >= 0 } {
set noiter [expr {$noiter%11}]
set colour [lindex {white lightblue blue green yellow orange red purple magenta black} $noiter]
} else {
set colour black
}
$image put $colour -to $xpix $ypix
}
#
# Create the canvas and the image and fill it
#
set width 200
set height 200
canvas .c -width $width -height $height
pack .c -fill both
set image [image create photo -width $width -height $height]
$image blank
.c create image 0 0 -image $image -anchor nw
set cdx [expr {4.0/$width}]
set cdy [expr {4.0/$height}]
proc mandelbrot_row {cdx cdy row width height} {
set cy [expr {-2.0+$cdy*$row}]
for {set col 0} {$col < $width} {incr col} {
set cx [expr {-2.0+$cdx*$col}]
set zx 0.0
set zy 0.0
set noiter [det_iteration $zx $zy $cx $cy 200]
setpixel $::image $col $row $noiter
}
if { $row < $height } {
after 1 [list mandelbrot_row $cdx $cdy [incr row] $width $height]
}
}
proc julia_row {cx cy zdx zdy row width height} {
set zy [expr {-2.0+$zdy*$row}]
for {set col 0} {$col < $width} {incr col} {
set zx [expr {-2.0+$zdx*$col}]
set noiter [det_iteration $zx $zy $cx $cy 200]
setpixel $::image $col $row $noiter
}
if { $row < $height } {
after 1 [list julia_row $cx $cy $zdx $zdy [incr row] $width $height]
}
}
set row 0
after 1 [list mandelbrot_row $cdx $cdy $row $width $height]
#set cx 0.0
#set cy 0.75
#after 1 [list julia_row $cx $cy $cdx $cdy $row $width $height]]