#!/usr/local/bin/wish
catch {rename send {}}

global copyright Program
set Program "mandelstep"
set copyright "$Program v0.4 Copyright (c) 1997 Karl J. Runge"

set TODO "

Zoom in and select Q's with high resolution.

Package for others to use, FractFile internally somehow? (DONE on unix...)

ConnectPoints switch will go back over current run and 
add/delete the lines?

Stop faster if user clicks mouse during Run action

(DONE) Infinity check for Step?

"

proc make_menubar {} {				# MAKE THE MENUBAR AT TOP

	global env; include;

	# make main window

	frame $MenuBar \
		-relief raised \
		-borderwidth 1;

	if {$IsApplet} {
		return [make_applet_buttons]
	}
	
	# make components of menubar

	###########
	# Actions
	###########

	menubutton $MenuBar.actions \
		-text "Actions" \
		-menu $MenuBar.actions.m \
		-font $font \
		-underline 0;

	menu $MenuBar.actions.m

	   $MenuBar.actions.m add command \
		-label "Long Run" \
		-font $fontMenu \
		-underline 0 \
		-command {long_run 5}

	   $MenuBar.actions.m add command \
		-label "X-Y Trace" \
		-font $fontMenu \
		-underline 4 \
		-command {run_history}


	   $MenuBar.actions.m add command \
		-label "Clear Last Orbit" \
		-font $fontMenu \
		-underline 0 \
		-command {clear_it}

	   $MenuBar.actions.m add separator

	   $MenuBar.actions.m add command \
		-label "Exit" \
		-font $fontMenu \
		-underline 1 \
		-command {util_quit}

	###########
	# Options
	###########

	menubutton $MenuBar.opts \
		-text "Options     " \
		-menu $MenuBar.opts.m \
		-font $font \
		-underline 0;

	menu $MenuBar.opts.m

	   $MenuBar.opts.m add checkbutton \
		-label "Connect Points" \
		-font $fontMenu \
		-underline 0 \
		-variable ConnectPoints

	   $MenuBar.opts.m add command \
		-label "Set N_iterations" \
		-font $fontMenu \
		-underline 4 \
		-command {set_n_iter}

	   $MenuBar.opts.m add command \
		-label "Set Delay" \
		-font $fontMenu \
		-underline 4 \
		-command {set_delay}

	###########
	# Help
	###########

	menubutton $MenuBar.help \
		-text "Help" \
		-menu $MenuBar.help.m \
		-font $font \
		-underline 0;
	menu $MenuBar.help.m \
		-tearoff 0;

	   $MenuBar.help.m add command \
		-label "Howto" \
		-command {util_help} \
		-font $font \
		-underline 0;

	   $MenuBar.help.m add command \
		-label "About" \
		-command {util_about} \
		-font $font \
		-underline 0;

	# skip $MenuBar.addkey 

	tk_menuBar \
		$MenuBar \
		$MenuBar.actions \
		$MenuBar.opts \
		$MenuBar.help

	tk_bindForTraversal .;

	make_top_buttons;
	make_top_entries;


	pack \
		$MenuBar.actions \
		$MenuBar.opts \
		$MenuBar.x $MenuBar.y $MenuBar.step \
		$MenuBar.run $MenuBar.stop $MenuBar.clear \
		-side left;

	pack \
		$MenuBar.help \
		-side right;
}

proc make_top_buttons {} {
	include;
	
	button $MenuBar.step \
		-text "Step" \
		-command {step_it} \
		-bd $button_bd \
		-padx $button_padx -pady $button_pady \
		-font $font

	button $MenuBar.run \
		-text "Run" \
		-command {run_it} \
		-bd $button_bd \
		-padx $button_padx -pady $button_pady \
		-font $font

	button $MenuBar.stop \
		-text "Stop" \
		-command {stop_it} \
		-bd $button_bd \
		-padx $button_padx -pady $button_pady \
		-font $font

	button $MenuBar.clear \
		-text "Clear" \
		-command {clear_it all} \
		-bd $button_bd \
		-padx $button_padx -pady $button_pady \
		-font $font
}

proc make_top_entries {} {
	include;
	
	make_entry $MenuBar.x "X: " Entry_X;
	make_entry $MenuBar.y "Y: " Entry_Y;

	set x_entry $MenuBar.x.entry
	set y_entry $MenuBar.y.entry

#	$x_entry icursor end
#	$y_entry icursor end

	bind $x_entry <Tab> "focus $y_entry; $y_entry icursor end"
	bind $y_entry <Tab> "focus $x_entry; $x_entry icursor end"

	bind $x_entry <Enter> "set Update_XY 0; focus %W"
	bind $y_entry <Enter> "set Update_XY 0; focus %W"

	bind $x_entry <Return> "setup_iteration_from_entry"
	bind $y_entry <Return> "setup_iteration_from_entry"

	bindtags $x_entry "all . Entry $x_entry"
	bindtags $y_entry "all . Entry $y_entry"
}

proc make_applet_buttons {} {
	include;
	make_top_buttons;
	make_top_entries;

	pack \
		$MenuBar.x $MenuBar.y $MenuBar.step \
		$MenuBar.run $MenuBar.stop $MenuBar.clear \
		-side left;
}

proc set_n_iter {} {
	get_query "Enter N_iterations: " N_iterations 4
}

proc set_delay {} {
	get_query "Enter Delay(millisec): " Delay 5
}

proc get_query {prompt varname {width ""}} {
	include;

	global QueryVar WaitVar

	if {$width == ""} {
		set width 5
	}

	eval set QueryVar \$$varname
	set WaitVar 0

	set query $MenuBar.query
	make_entry $query "     $prompt" QueryVar $width

	bind $query.entry <Return> "set WaitVar 1; destroy $query"

	pack $query -side left;

	$query.entry icursor end
	$query.entry selection range 0 end
	focus $query.entry

	tkwait variable WaitVar

	if {$QueryVar != ""} {
		set $varname $QueryVar
		set_message "Set $varname to $QueryVar"
	} else {
		set_message "Not setting $varname"
	}
}

proc make_entry {widget label varname {width ""}} {	# MAKE ENTRYBOX
	include
	
	frame $widget -bd 0m; 

	label $widget.label \
		-font $fontMenu

	$widget.label configure \
		-text $label

	if {$width == ""} {
		set width $XY_Entry_Width
	}

	entry $widget.entry \
		-relief sunken \
		-width $width \
		-font $fontMenu \
		-textvariable $varname;

	bind $widget.entry <Return> {run_command "" expand}
	bind $widget.entry <Control-u> "$widget.entry delete 0 end"
	bind $widget.entry <Control-e> "$widget.entry insert insert {2>&1 }"

	bind $widget.entry <Enter>	{focus %W}

	bindtags $widget.entry "Entry $widget.entry . all"

        pack $widget.label \
		-side left \
		-fill x \
		-expand 0;

        pack $widget.entry \
		-side left \
		-fill x \
		-expand 1;
}

proc make_canvas {} {
	include;

	create_image $Image;

	if {$OS == "unix" && ! $IsApplet} {
		puts stderr "creating image, this may be slow..."
	}

	set w [image width $Image]
	set h [image height $Image]

	set Canvas_width  $w
	set Canvas_height $h
	set Canvas_x_factor [expr "$Fract_x_width/$Canvas_width"];
	set Canvas_y_factor [expr "$Fract_y_width/$Canvas_height"];
	set Float_x_factor  [expr "$Canvas_width/$Fract_x_width"];
	set Float_y_factor  [expr "$Canvas_height/$Fract_y_width"];

	canvas $Canvas \
		-relief groove \
		-width $w \
		-height $h;
	$Canvas create image 0 0 \
		-anchor nw \
		-image $Image;

	bind $Canvas <Motion> "xy_update %x %y";
	bind $Canvas <1> "setup_iteration %x %y";
	bind $Canvas <Enter> "set Update_XY 1; focus %W";

}

proc xy_update {ix iy} {
	global Fract_x_min Fract_y_min;
	global Canvas_x_factor Canvas_y_factor;
	global Entry_X Entry_Y Update_XY;

	if {! $Update_XY } {
		return;
	}

	set x [i_to_f x $ix]
	set y [i_to_f y $iy]

	set Entry_X $x;
	set Entry_Y $y;
}

proc setup_iteration_from_entry {} {
	include;
	set ix [f_to_i x $Entry_X]
	set iy [f_to_i y $Entry_Y]

	setup_iteration $ix $iy

}

proc setup_iteration {ix iy} {
	include;
	global StopRun

	set StopRun 1

	if {$RunIsOn} {
		util_error "Run Interrupted!";
		update; after 200; update;
		return;
		
	}
	set Update_XY 0;
	

	set x [i_to_f x $ix]
	set y [i_to_f y $iy]

	set Entry_X $x;
	set Entry_Y $y;

	set Q_x $x;
	set Q_y $y;

	global Q_msg
	set Q_msg "Starting pt: Q_x: $Q_x	Q_y: $Q_y";
	wm_comment $Q_msg

	set Curr_Run_previous_x $x;
	set Curr_Run_previous_y $y;
	set Curr_Run_x $x;
	set Curr_Run_y $y;

	incr RunCount;
	set IterCount 0

	set RunTagsList($RunCount) {}
	set RunCoordsList($RunCount) "x: $x	y: $y\n"

	set tag [make_point $ix $iy $PointStartColor];
	set FirstPoint $tag
	set LastPoint "First"
	lappend RunTagsList($RunCount) $tag

}

proc step_it {} {
	iterate;

	if [check_infinity] {
		global IterCount xy_msg
		util_error "To Infinity and Beyond! ($IterCount) $xy_msg"
	}
}

proc long_run {n} {
	global N_iterations
	set n [expr "$n * $N_iterations"]
	run_it $n;
}

proc run_it {{n ""}} {
	global Delay N_iterations StopRun IterCount xy_msg
	global RunIsOn

	if {$n == ""} {
		set n $N_iterations
	}
	set StopRun 0

	set RunIsOn 1
	for {set i 0} {$i < $n} {incr i} {
		if {$StopRun} {
			set_message "Run Stopped!" "" "yes"
			break;
		}
		iterate;
		after $Delay;
		if [check_infinity] {
			util_error "To Infinity and Beyond! ($IterCount) $xy_msg"
			break;
		}
	}
	set RunIsOn 0
}

proc stop_it {} {
	global StopRun RunIsOn
	set StopRun 1
	if {! $RunIsOn} {
		set_message "No Run in progress."
	}
}

proc iterate {} {
	global Curr_Run_x Curr_Run_y
	global Curr_Run_previous_x Curr_Run_previous_y

	global ConnectPoints LastPoint Canvas PointColor PointCurrentColor

	global RunCount IterCount RunTagsList RunCoordsList LineColor
	global xy_msg

	set x_old $Curr_Run_x
	set y_old $Curr_Run_y

	set Curr_Run_x [map x $x_old $y_old]
	set Curr_Run_y [map y $x_old $y_old]

	set xy_msg "x: $Curr_Run_x	y: $Curr_Run_y"
	set_message "Current position($IterCount):	$xy_msg" "noprefix"
	
	append RunCoordsList($RunCount) "$xy_msg\n";

	set local_debug 0;

#	if {$local_debug} {
#		puts "=================================="
#		puts "old x: $x_old";
#		puts "old y: $y_old";
#		puts "new x: $Curr_Run_x";
#		puts "new y: $Curr_Run_y";
#	}

	set ix [f_to_i x $Curr_Run_x]
	set iy [f_to_i y $Curr_Run_y]

#	if {$local_debug} {
#		puts "ix: $ix";
#		puts "iy: $iy";
#	}

#	puts "LastPoint: $LastPoint"
	if {$LastPoint != "First" && $LastPoint != ""} {
#		puts "doing: $LastPoint";
		$Canvas itemconfigure $LastPoint \
			-fill $PointColor \
			-outline ""
	}

	incr IterCount

	lappend RunTagsList($RunCount) \
		[list [make_point $ix $iy $PointCurrentColor]];

	if {$ConnectPoints} {
		set ix_old [f_to_i x $x_old]
		set iy_old [f_to_i y $y_old]

		lappend RunTagsList($RunCount) \
			[make_line $ix_old $iy_old $ix $iy $LineColor]
	}

	set Curr_Run_previous_x $x_old
	set Curr_Run_previous_y $y_old

}

proc f_to_i {which coord}  {
	global Canvas_width Canvas_height
	global Canvas_x_factor Canvas_y_factor
	global Float_x_factor Float_y_factor
	global Fract_x_min Fract_x_width Fract_y_min Fract_y_width;

	if {$which == "x" } {
		set i [expr "int(($coord - $Fract_x_min)*$Float_x_factor)"]
		return $i;
		
	} elseif {$which == "y"} {
		set i [expr "int(($coord - $Fract_y_min)*$Float_y_factor)"]
		return $i;

	} else {
		return "ERROR";
	}
}

proc i_to_f {which coord}  {
	global Canvas_width Canvas_height
	global Canvas_x_factor Canvas_y_factor
	global Float_x_factor Float_y_factor
	global Fract_x_min Fract_x_width Fract_y_min Fract_y_width;

	if {$which == "x" } {
		set f [expr "$Fract_x_min + ${Canvas_x_factor}*${coord}"]
		return $f;
		
	} elseif {$which == "y"} {
		set f [expr "$Fract_y_min + ${Canvas_y_factor}*${coord}"]
		return $f;

	} else {
		return "ERROR";
	}
}

proc map {coord x y} {
	# This is specific to Classical Mandelbrot Map
	global Q_x Q_y
	if {$coord == "x"} {
		return [expr "${x}*${x} - ${y}*${y} + $Q_x"]
	} elseif {$coord == "y"} {
		return [expr "2*${x}*${y} + $Q_y"]
	}
}

proc check_infinity {} {
	global FractInfinity_x FractInfinity_y
	global Curr_Run_x Curr_Run_y

	if { $Curr_Run_x < -$FractInfinity_x } {
		return 1;
	} elseif { $Curr_Run_x > $FractInfinity_x } {
		return 1;
	} elseif { $Curr_Run_y < -$FractInfinity_y } {
		return 1;
	} elseif { $Curr_Run_y > $FractInfinity_y } {
		return 1;
	} else {
		return 0;
	}
	
}

proc make_point {ix iy {color ""} {size ""}} {
	global Canvas PointColor PointSize
	global RunCount IterCount
	global LastPoint;

	if {$color == ""} {
		set color $PointColor;
	}
	if {$size == ""} {
		set size $PointSize
	}

	set point_name "point_${RunCount}_${IterCount}"

	set id [$Canvas create oval \
		[expr "$ix - $size"] [expr "$iy - $size"] \
		[expr "$ix + $size"] [expr "$iy + $size"] \
		-fill $color \
		-outline "" \
	]

##	$Canvas raise $id

	$Canvas addtag $point_name withtag $id 

	set LastPoint $point_name;

	update;

	return "$point_name"
}

proc make_line {x1 y1 x2 y2 {color ""}} {
	global Canvas PointColor LineSize
	global RunCount IterCount

	if {$color == ""} {
		set color $PointColor;
	}

	set line_name "line_${RunCount}_${IterCount}"

	set id [$Canvas create line \
		$x1 $y1 $x2 $y2 \
		-fill $color \
	]

##	$Canvas raise $id

	$Canvas addtag $line_name withtag $id 

	update;

	return "$line_name"
}

proc clear_it {{which ""}} {
	include;

	if {$which == "all"} {
		if [info exists RunTagsList] {
		    foreach i [array names RunTagsList] {
			if {$i != "all"} {
				clear_it $i
			}
		    }
		}

		return 1;
	}

	if {$which == ""} {
		set which $RunCount;
	}

	if [info exists RunTagsList($which)] {
		
	    foreach tag $RunTagsList($which) {
		$Canvas delete $tag;
	    }

	    unset RunTagsList($which);
	}
}

proc run_history {} {
	global RunCount RunCoordsList Q_msg

	if {$RunCount == "0"} {
		util_error "No Runs Yet!"
		return;
	}

	set text $RunCoordsList($RunCount);

	make_toplevel_text \
		.hist_$RunCount \
		$text \
		$Q_msg \
		"40"
}
					# MAKE A TOPLEVEL TEXT AREA
proc make_toplevel_text { \
	w \
	text \
	{title ""} \
	{width 80} \
	{height 30} \
	{do_help ""} \
		} {
				# should combine code with "make_text"
				# somedate
	global font fontSmall fontBig fontMenu fontTextWindow
	global HelpText IsApplet

	if {$width == ""} {
		set width 80
	}
	if {$height == ""} {
		set height 30
	}
	
	set relief "groove"

	catch "destroy $w"
	toplevel $w

	if {$title != ""} {
		if { !$IsApplet } {
			wm title $w $title
		} else {
			set_message $title
		}
	}

	set wf $w.frame
	frame $wf

	set textWidget $wf.text
	set HelpText $textWidget

	if {$do_help != ""} {

		set mf $wf.menu

		frame $mf \
			-relief $relief;

		menubutton $mf.menu \
			-text "Topics" \
			-menu $mf.menu.m \
			-font $font;
	#		-relief groove \

		set bf_relief "raised"
		set bf_border 1


		button $mf.back \
			-text "<-" \
			-command {AdjustHelpHistory} \
			-relief $bf_relief \
			-bd $bf_border \
			-font $font;

		button $mf.forward \
			-text "->" \
			-command {AdjustHelpHistory forward} \
			-relief $bf_relief \
			-bd $bf_border \
			-font $font;

		menu $mf.menu.m;

		set count 0

		set old_text $text
		set text ""

		foreach line [split $old_text "\n"] {
			incr count
			if [regexp "%%(.*)%%" $line range mVar] {
			    regsub -all {%%} $line {} line
			    if [regexp {^_} $mVar] {
				regsub -all $mVar $line {} line
				regsub {^_} $mVar {} mVar
			    }
			    if [regexp {^\^s} $mVar] {
				regsub -all {^\^s} $mVar {  } mVar
				regsub -all {^\^s} $line {} line
			    }
			    $mf.menu.m add command \
				-label "$mVar" \
				-command "$textWidget yview $count.0; HelpHistory $count.0" \
				-font $fontMenu
			}
			set text "${text}${line}\n";
		}
		$mf.menu.m add separator 
		$mf.menu.m add command \
			-label "Dismiss" \
			-command "destroy $w" \
			-font $fontMenu

		pack $mf.menu $mf.back $mf.forward \
			-side left \
			-expand 0; 


		pack $mf \
			-side top \
			-fill x \
			-expand 0; 
	}

	scrollbar $wf.scrolly \
		-relief sunken \
		-command "$textWidget yview"

	text $textWidget \
		-width $width \
		-height $height \
		-setgrid 1 \
		-yscrollcommand "$wf.scrolly set" \
		-relief $relief \
		-bd 2 \
		-font $fontTextWindow;

	button $wf.dismiss \
		-text "Dismiss" \
		-command "destroy $w" \
		-font $fontSmall

	pack $wf.dismiss \
		-side bottom \
		-fill x \
		-expand 0; 

	pack $wf.scrolly \
		-side right \
		-fill y \
		-expand 0; 

	pack $textWidget \
		-side top \
		-fill both \
		-expand 1;

	bind $textWidget <Control-x> {%W delete sel.first sel.last};
#	bind $textWidget <2> {%W insert insert [selection get]; %W yview -pickplace insert}
	bind $textWidget <B2-ButtonRelease> {%W yview insert}; 	# Should Fix someday

	bind $textWidget <Enter> {focus %W}
	bind $textWidget <Escape> "destroy $w"
	bind $w          <Escape> "destroy $w"

	bindtags $textWidget "Text . all $textWidget"

	if {$text != ""} {
		$textWidget insert 0.0 $text
	}

	pack $wf \
		-fill both \
		-expand 1;


	util_center_window $w
	
}

proc HelpHistory {index} {
	global HelpCount HelpHistList HelpLocation

	if ![info exists HelpCount] {
		set HelpCount 0
	} elseif {$index == $HelpHistList($HelpLocation)} {
		return
	}

	incr HelpCount

	set HelpHistList($HelpCount) $index
	set HelpLocation $HelpCount
}

proc AdjustHelpHistory {{direction "back"}}  {

	global HelpCount HelpHistList HelpLocation HelpText

	if {![info exists HelpLocation] || $HelpLocation == "0"} {
		return
	}

	if {$direction == "back"} {
		set new [expr "$HelpLocation - 1"]
		if {$new < 1} {set new 1} 
	} elseif {$direction == "forward" } {
		set new [expr "$HelpLocation + 1"]
		if {$new > $HelpCount} {set new $HelpCount} 
	}
	
	set HelpLocation $new
	$HelpText yview $HelpHistList($new)
}

proc make_message {} {			# MAKE THE MESSAGE AREA AT BOTTOM
	include;

	label $Label \
		-font $fontSmall \
		-relief groove \
		-anchor w;

	set_message "Welcome to $Program!" "noprefix"
}

proc set_message {{msg} {flag prefix} {flash no}} {
					# SET THE MESSAGE AREA TEXT
	global Label msg_prefix msg_flash generalBackground
	global Msg_width

	if {$flag == "prefix"} {
		set WidthMax [expr "$Msg_width - 19"]
	} else {
		set WidthMax [expr "$Msg_width - 9"]
	}

	if ![winfo exists $Label] {
		return
	}

	if {[string length $msg] > $WidthMax} {
		set msg [string range $msg 0 $WidthMax];
		set msg "$msg...\""
	}

	if {$msg != "NO_MSG"} {
		if { $flag == "noprefix" } {
			$Label configure \
				-text "$msg"
		} else {
			$Label configure \
				-text "$msg_prefix $msg"
		}
	}

	if { $flash == "flash" || $flash == "yes" } {
		$Label configure -background $msg_flash
		update; after 600;
		$Label configure -background $generalBackground
#		update; after 200
#		$Label configure -background $msg_flash
#		update; after 200
#		$Label configure -background $generalBackground
	}
	update;
}

proc flash_message {} {			# FLASH THE MESSAGE BOX
	set_message "NO_MSG" "" "flash"
}

proc stop_watch {x} {		# MAKE CURSOR A WATCH WHEN USER SHOULD WAIT
	global  Entry;
	if { $x == "on" } {
		. config -cursor {watch}
		update
	} else {
		. config -cursor {}
#		$Entry.entry config -cursor {xterm}
		update
	}
}

proc wm_comment {{comment ""} {both 0}} {
	global Program IsApplet

	
	if {$comment == ""} {
		set comment $Program
	} else {
		if {$both} {
			set comment "$Program ($comment)"
		} else {
			set comment "($comment)"
		}
	}

	if {$IsApplet} {
		set_message $comment;
	} else {
		wm title . $comment;		# Window Manager's title
	}
}

proc util_center_window {w} {   # CENTER A WINDOW IN MIDDLE OF SCREEN

	global IsApplet;

	if {$IsApplet} {
		return;
	}

        wm withdraw $w
        update idletasks
        set x [expr [winfo screenwidth $w]/2 - [winfo reqwidth $w]/2 ]
	if {$w != "."} {
		set x [expr "$x - [winfo vrootx [winfo parent $w]]"]
	}
        set y [expr [winfo screenheight $w]/2 - [winfo reqheight $w]/2 ]
	if {$w != "."} {
		set x [expr "$x - [winfo vrooty [winfo parent $w]]"]
	}
        wm geom $w +$x+$y
        wm deiconify $w
}

# proc include std global variables

proc include {} {		# "COMMON BLOCK" OF GLOBAL VARIABLES

    uplevel {

	# Globals:

	global Fract_x_min Fract_x_width Fract_y_min Fract_y_width FractFile;
	global FractInfinity_x FractInfinity_y
	global Entry_X Entry_Y;

	global Debug

	global font fontSmall fontBig fontReg fontRegSmall;
	global fontMenu fontMenuLarge fontMenuSmall fontMenuVerySmall;
	global fontTextWindow

	global PointStartColor PointColor PointCurrentColor PointSize
	global LineColor LastPoint FirstPoint
	global RunTagsList RunCoordsList;
	global RunCount IterCount RunIsOn

	global Update_XY

	global Q_x Q_y
	global Curr_Run_x Curr_Run_y
	global Curr_Run_previous_x Curr_Run_previous_y

	global Delay N_iterations

	global ConnectPoints
	global debug;

	global Program my_name;

	global generalBackground genBG genBGLight genActBG genSelBG Green
	global WarningColor
	global XY_Entry_Width

	global Canvas Image
	global Canvas_width Canvas_height
	global Canvas_x_factor Canvas_y_factor
	global Float_x_factor Float_y_factor
	global MenuBar
	global Label msg_prefix msg_flash

	global Text_height Text_width Msg_width


	global tk_version tcl_platform OS IsApplet;

	global button_bd button_padx button_pady

	global OutsideWorld

    # end of up level source
    }

# end of procedure
}

proc initialize {} {		# INITIAL "COMMON BLOCK" OF GLOBAL VARIABLES

   # do following script up one level

    uplevel {


	# Initialize Globals:

	set Canvas ".canvas";
	set Image "main";
	set Fract_x_min		"-2.75";
	set Fract_x_width	"4.00";
	set Fract_y_min		"-1.25";
	set Fract_y_width	"2.50";
	set FractFile		"mandelstep.gif";
	set FractFileDOS	"mandlstp.gif"

	set FractInfinity_x "10.0"
	set FractInfinity_y "10.0"

	set PointStartColor "blue"
	set PointColor "green"
	set PointCurrentColor "red"
	set PointSize 2

	set OutsideWorld "INSIDE_WORLD"

	if { $IsApplet && $OutsideWorld != "OUTSIDE_WORLD" } {
		set PointSize 1
	}
	if { $IsApplet } {
		set PointSize 1
	}

	set LastPoint ""
	set FirstPoint ""
	set LineColor "gray"

	set RunCount 0
	set RunIsOn 0
	set IterCount 0
	set Update_XY 1

	set ConnectPoints 1

	set Delay 10
	set N_iterations 30;

	set Text_height 33
	set Text_width  85
	set Msg_width  120

	set font -adobe-helvetica-bold-r-*-*-*-140-*-*-*-*-*-*;
	set fontSmall -adobe-helvetica-bold-r-*-*-*-120-*-*-*-*-*-*;
	set fontBig -adobe-helvetica-bold-r-*-*-*-180-*-*-*-*-*-*;
	set fontReg -adobe-helvetica-medium-r-*-*-*-120-*-*-*-*-*-*;
	set fontRegSmall -adobe-helvetica-medium-r-*-*-*-100-*-*-*-*-*-*;
	set fontRegVerySmall -adobe-helvetica-medium-r-*-*-*-80-*-*-*-*-*-*;

	set Debug "1"

	if { $OS == "windows" } {
		set font "Arial"
		set fontSmall "Arial"
		set fontReg "Arial"
		set fontRegSmall "Arial"
		set fontRegVerySmall "Arial"

		set FractFile $FractFileDOS
	}

	set fontMenuLarge $font
#	set fontMenuSmall $fontReg
	set fontMenuSmall $fontSmall
	set fontTextWindow "fixed"
	set fontMenuVerySmall $fontRegSmall

	set fontMenu $fontMenuSmall

	set debug 1;

	set XY_Entry_Width "12";

	set MenuBar .menubar
	set Label .label
	set msg_prefix "Status:";
	set msg_flash "white";

	set startGeom "+10+10"

	if { $OS == "windows" } {
		set msg_flash "$genActBG";
	}

	set WarningColor {light yellow}

	set button_bd 2
	set button_padx 2
	set button_pady 1


    # end of uplevel
    }

# end of procedure
}

#proc wm {{a ""} {b ""}  {c ""}  {d ""}  {e ""}  {f ""}  {g ""} } {
#	puts stderr "wm args: $a $b $c $d $e $f $g";
#}

proc util_check_platform {} {	# DETERMINE PLATFORM WE ARE RUNNING ON
	
	global tcl_platform OS IsApplet argv0 embed_args;

	set OS "unix"
	set IsApplet "0";

#	if { [info exists argv0] && $argv0 == "tclPlugin" } {
#		set IsApplet "1";
#	}
	if { [info exists embed_args] } {
		set IsApplet "1";
	}

	if { [info exists tcl_platform(platform)] } {

		if { [info exists tcl_platform(osVersion)] } {
			set osv  $tcl_platform(osVersion)
		} else {
			set osv "4.1"
		}

		if { $tcl_platform(platform) == "windows" \
		    && $osv < "4.0" } {

			set OS "windows"

		} elseif { $tcl_platform(platform) == "windows" \
		    && $osv >= "4.0" } {

			set OS "win95"

		} elseif { $tcl_platform(platform) == "unix" } {

			set OS "unix"

		} elseif { $tcl_platform(platform) == "macintosh" } {

			set OS "macintosh"
		}
	}
	# puts stdout "set OS to $OS: $tcl_platform(platform), $tcl_platform(osVersion)"
}

proc os_is_dos {} {		# DETERMINE IF PLATFORM IS DOS
	global OS

	if [regexp {^win} $OS] {
		return 1
	} else {
		return 0
	}
}

proc util_about {} {		# SET MESSAGE AT BOTTOM TO COPYRIGHT

	global copyright
	set_message $copyright "noprefix" "flash";
}

proc util_help {{where "toplevel"}} {		# PRINT HOWTO INSTRUCTIONS

	global Program copyright
	set program "\"$Program\""

	set help_text \
"=====================
Basic Idea and Usage:%%_Basic Idea%%
=====================

Click on a point in the Mandelbrot set (technically the white areas). To
see *why* your point is in (or not in!) the set, Click on \"Run\" to
start the Mandelbrot iterations.  If the resulting \"orbit\" does not go
to infinity your starting point is in the Mandelbrot set, otherwise it
is not (and the color assigned to it on the background image indicates
in some sense how \"far away\" it is from the set).

The different regions of the fractal correspond to different kinds
of stable, closed orbits. Neat!!

========================
How to use ${program}:%%_How to Use%%
========================

$program IS NOT a fractal generator or zoomer.

Excellent programs for doing generation can be found. For example:

  Fractint:       http://spanky.triumf.ca/www/fractint/FRACTINT.HTML
  Xmandel:        http://chem.leeds.ac.uk/ICAMS/people/zsolt/xmandel.html
  XaoS:           http://www.paru.cas.cz/~hubicka/XaoS/

and there are others.

Fractal generation programs want to do as many pixel calculations
as fast as possible, $program, on the other hand, wants to do as
few pixel calculations as slowly as possible!!!!

===============
Huh? Why Slow?%%_Why Slow?%%
===============

Fractals are beautiful and mysterious things to look at, but if you want
to at least start to try understand a little bit about them, the fractal
generation programs (out of necessity) hide too much information.  They
basically give the bottom line: is a point in the fractal set or not,
and if not, color it to show how in a crude sense how \"far away\" it is
from the set.

Since there can easily be half a million pixels, each requiring 100-200,
or more, iterations each, it is very useful that the fractal generation
programs do not show all the information contained in the iteration
\"trajectories\".

The idea behind $program is that by letting a person select starting
positions and looking at a handful of iteration \"trajectories\" or
\"orbits\" the person can begin to understand more about the different
regions of the Mandelbrot set. I.e., not just whether a point is inside
the set, but what sort of \"dance\" it does to be a member. It is not
long before one is using one's intuition about what sort of \"dance\"
a point will do before one runs the actual iteration. It's a puzzle.
It's fun!

=========
Mappings:%%_Mappings%%
=========

For many fractals, the X-Y plane describes a control parameter of an
iterated mapping function.  If, for a fixed value of the control
parameter, repeated iteration leads to the coordinates diverging towards
infinity that point is said to not be in the fractal set.  How fast it
diverges to infinity is usually used to determine what color is assigned
to it. This gives beautiful images!

A point that does not lead to divergence toward infinity is said to be
in the fractal set (in practice, if it has not diverged after some pre-
defined \"large enough\" value, i.e.  N_MAX = 128, then for practical
purposes it is said that the point is in fractal set, although who knows
exactly what will happen in the next N_MAX iterations!).  Typically a point
declared to be in the set would be colored black or white. They are white
for $program.

For the classical Mandelbrot set the iterated mapping function is:

	x' = x^2 - y^2 + Q_x
	y' = 2xy       + Q_y

or in complex numbers notation, (z = x + iy):

	z' = z^2 + Q

The prime, e.g. x', means the updated value after one iteration.
Perhaps x <==  x^2 - y^2 + Q_x, y <== 2xy + Q_y is a better notation.

Q = (Q_x, Q_y) is the control parameter of the iterated mapping
function.  A Q value is in the Mandelbrot set if (starting the first
iteration at z = (0,0)) after infinitely many iterations the z variable
has not diverged to infinity.

It is not hard to show that if |z| > 2 then z will quickly diverge to infinity.


========
Running:%%_Running%%
========

When $program starts up (it even does that slowly!) it will show you
the complex Q plane with the classical Mandelbrot fractal (derived via
XaoS mentioned above) superimposed on the background. A little black
dot denotes Q = (0,0). white regions denote the points inside the set (i.e.
iteration does not diverge for those points).

OK, here are the steps to actually run something:

   Click the mouse somewhere to select a point Q.

   To do a single iteration step from starting a z = Q, click the
   \"Step\" button.

   Or to run a whole bunch, say 30, in succession, click on \"Run\".

That is basically it. 

For a Q-point to be in the Mandelbrot set it seems (to me) that it must
converge to a stable n-cycle orbit.  That is to say, an orbit that
repeats after n iterations.  The biggest round white region (the one
containing 0,0) is where the iteration evolves to a 1-cycle.  Try it and
see!  The next largish section that is a circle to the left of the 1-
cycle region is where 2-cycles are stable.  Crossing over a boundary
inside the Mandelbrot set usually means an n-cycle region has become
unstable and an m-cycle has become stable.

It's fun predicting (at least I find it fun!) what the cycle lengths will
be for a given region.  Also, the shape of the orbit will sometimes be
surprising. Run in the 1-cycle region close to another region and see
how the shape of slowest dying transient (as the orbit collapses to a point)
lets you predict the cycle length and orbit shape of the nearby region without
even running in it!

$program does not (yet) let you get into the fascinating \"super deep
zooms\" regions that give the beautiful images.  But many things can be
learned from looking at the global iteration picture.  Can your
intuition learned at the global level be applied way down in the deep
zoom regions?  It is, afterall, a self similar fractal!


-----------------------------------------------------------------------------
Now to touch upon all the features, buttons, etc.


=================
Menu Bar Buttons:%%_Menu Bar%%
=================

%%^sStep%%:
-----

On the main menubar the \"Step\" button will perform one iteration of
the mapping function.


%%^sRun%%:
----
 
The next button over \"Run\", will do a number (default 30) of iterations
in succession. The starting point is blue, the latest point is red, and
the rest are green. Follow the red dot for the orbit.

%%^sStop%%:
-----

As the name implies, this button will stop the current \"Run\". Hit
\"Run\" again to resume, or switch to a new set of run parameters if
you like.

%%^sClear%%:
------

This will remove all trajectories/orbits from the display.
(See \"Clear Last Orbit\" below)

%%^sHelp%%:
-----

Shows the current help text.

%%^sX: and Y:%%
---------

As the mouse is moving around the fractal background, the Q_x and Q_y
of the mouse position are shown in these entry boxes.

If you click the mouse button the Q-value at point of the click will be
\"frozen\" in the display boxes.  You can then, say, move the mouse over
to the \"Run\" button.

You can also type values directly into the X: and Y: entry boxes. Hit
<Return> in either one to \"freeze/set\" the values, then go over to 
\"Step\" or \"Run\" to start iterating the mapping function for this Q.

========
Actions:%%_Actions%%
========

	More things one can do.

%%^sLong Run%%:
---------

Do a run 5 times the normal length.

%%^sX-Y Trace%%:
------------

Pops up a text window with the history of x and y values for the latest run.

%%^sClear Last Orbit%%:
----------

Remove the latest trajectory/orbit from the display.

%%^sExit%%:
-----

I forget what this one does :-)

======================
Options:%%_Options%%
======================

	Set the parameters.

%%^sConnect Points%%:
---------------

Checkbox to set mode to draw lines between the iteration points or not.

%%^sSet N iterations%%:
-----------------

Set the number of iterations in one \"Run\" click. An entry box will appear
on the Menu Bar. Type the value in the entry box and then hit <Return> to
set it.

%%^sDelay%%:
------

Set the time delay between iterations in the \"Run\" action.  Not that
$program is blazingly fast or anything, but you may want to slow it down
a bit to watch some complicated orbit.  Enter the delay time in
milliseconds.  There are 1000 of them in 1 second.  As in the previous
paragraph, the entry box appears on the Menu Bar, Hit <Return> to set
the value to what you typed in.


=============================================================================

Well, that's all for now except for some misc. notes below.
Please send suggestions, comments, etc to me at runge@crl.com

The main thing on the TODO list is: 
	Let user drag out a region of the plane with the mouse,
	a second canvas appears where the region is zoomed
	(maybe call xaos or something in \"filter\" mode, or just scale?)
	Then the user can click on the expanded view to select the
	starting point with higher resolution. Iterations should
	be shown on both the main and zoomed canvases.


$copyright


=============================================================================

%%^sMisc. Notes%%:
------------

One can solve for the two main regions of the classical Mandelbrot set
by solving using some simple math: 

If you denote the mapping by f(z) = z^2 + Q, then look for 
fixed point solutions  z = f(z), this will give a quadratic equation
for the 1-cycle orbit z's. By examining the derivative df/dz at the
fixed point one finds it is a stable orbit when |df/dz| < 1 (hint expand
about the solution z + dz and look for the condition that |dz| shrinks). 
The formula |df/dz| < 1 gives exactly the big cardioid shape that encloses
the point (0,0). Seriously cool!

What about the stable 2-cycle region? Look at fixed points z = f(f(z))
this will give you a quartic equation in z, but you can factor out
the 1-cycle solutions found above (since a 1-cycle is clearly also a
2-cycle), this leaves another quadratic equation to solve for the \"real\"
2-cycles. The condition that is it stable ( |d(f(f(z))/dz| < 1) gives the
equation for the circle (centered at (-1,0)) immediately to left of
the 1-cycle cardioid. The circle's radius is 1/4. 

Well, the math starts getting hard at z = f(f(f(z))), (3-cycles) and above,
but you can let $program do all the work for you! Start a run inside a 
given region and what what sort of n-cycle it settles into. 

In my non-rigorous view of these things, all of the infinitely many
sections of the mandelbrot fractal can be thought as some sort of stable
n-cycle.  As n goes up the region of stability gets smaller and smaller
giving rise to smaller still regions with longer period orbits.  And
this continues downward to smaller scales without limit.  Amazing!

Another way to proceed is to look for Super Stable orbits. These
are ones obeying the stability criterion: d(f(...(f(z))...)/dz = 0.
It turns out this requires one of the points on the orbit be z = 0.
The control parameters corresponding to these super stable orbits 
tend to be near the center of its region, i.e. farthest from the
region boundary (where |df(...)/dz| = 1). Anyway, it is not too hard to
get a symbolic manipulator work out f(f(...f(0)...)) = Q, then solve
numerically for the roots Q of this polynomial (it is all Q, no z for
this approach). Sure enough, the roots are right near the centers of the
corresponding n-cycle regions of the set.

"

	if {$where == "toplevel"} {
		global Program
		make_toplevel_text .help_window $help_text "Howto use \"$Program\"" "" "" "true"
	} else {
		;
	}
}

proc util_error {{message "Error occurred."}} {
				# REPORT ERROR TO MESSAGE BOX
	global IsApplet
	if { ! $IsApplet } {bell}
	set_message $message "" "flash"
}

proc util_quit {} {		# QUIT APPLICATION
	destroy .
}

proc app_defaults {} {		# SET UP APPLICATION DEFAULTS

	global my_name;
	global generalBackground genBG genSelBG genActBG genBGLight
	global tk_version tcl_platform OS

	set genBG grey80
	set genBGLight grey75
	set genSelBG grey70
	set genActBG grey65

	if { $OS == "windows" } {
		set genBG white
		set genSelBG	"#A4C8F0"
		set genBGLight	"#A4C8F0"
		set genActBG	"#A4C8F0"
	}

#	puts "genActBG $genActBG"

	set generalBackground $genBG;

	option add *selectBackground		$genSelBG
	option add *background			$genBG
	option add *activeBackground		$genActBG
	option add *frame*background		$genBG
	option add *scrolly*foreground		$genBG
	option add *scrolly*activeForeground	$genActBG
	option add *scrollx*foreground		$genBG
	option add *scrollx*activeForeground	$genActBG

	option add *Button*padX	2
	option add *Button*padY	2

	if { $OS == "windows" } {
		option add *Button*background		grey80
		option add *Button*activeBackground	grey80
		option add *highlightBackground		$genBG
		option add *frame*Background		$genBG
	}
	
}

proc create_image {image} {
	include;

	if {$IsApplet} {
		set data [small_gif_data];
		image create photo $image \
			-data [set data]
		return;
	}

	set file [dump_gif_file]

	image create photo $image \
		-file $file

	after 500

	if ![os_is_dos] {
		catch {file delete -force $file}
		if {$OS == "unix" && [file exists $file] && ! $IsApplet} {
			catch {exec rm -f $file}
		}
	}

	return
}

proc dump_gif_file {} {
	include;

	if { $IsApplet } {
		return [dump_gif_file_applet]
	} elseif {$OS == "unix"} {
		return [dump_gif_file_unix]
	} elseif [os_is_dos] {
		return [gif_file_dos]
	}
}

proc dump_gif_file_unix {} {
	global argv0 IsApplet;

	set pid [pid]
	set tmpfile "/tmp/mandelstep${pid}.gif"

	set in [open $argv0 r]
	set out [open "|uudecode" w]

	if { ! $IsApplet } {
		puts stderr "creating tmpfile $tmpfile..."
	}

	set on 0

	while {[gets $in line] > -1} {
		if {$on} {
			if [regexp {^begin} $line] {
				set line "begin 644 $tmpfile"
			}
			puts $out $line
			break;
		}
		if [regexp {^BEGIN_UU} $line] {
			set on 1
		}
	}
	while {[gets $in line] > -1} {
		if [regexp {^END_UU} $line] {
			break;
		}
		puts $out $line
	}
	close $out
	return $tmpfile
}

proc gif_file_dos {} {
	global argv0 FractFileDOS

	regsub -nocase {\.tcl$} $argv0 {.GIF} file

	if ![file exists $file] {
		set file [file tail $argv0]
		set file "$file/$FractFileDOS"
	}

	if ![file exists $file] {
		set file $FractFileDOS
	}
	return $file
}

proc small_gif_data {} {

# this is the 640x400 GIF in BASE64 format. So far, only the
# tcltk plugin can read this format.

set data {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}

return $data
	
}
proc very_small_gif_data {} {

set data {
removed to save space.
}

return $data
	
}
# MAIN starts here.

include;
util_check_platform;

set my_name [winfo name .];
app_defaults;

if {! $IsApplet } {
	wm withdraw .
}

initialize;

. configure \
	-background $generalBackground;		# someday fix...

wm_comment

if { ! $IsApplet} {
	wm geom . $startGeom;
	wm minsize . 1 1;
}

make_menubar;
make_canvas;

if { $IsApplet && $OutsideWorld == "OUTSIDE_WORLD" } {
	set OriginPointSize $PointSize
} else  {
	set OriginPointSize 1
}

make_point [f_to_i x "0.0"] [f_to_i y "0.0"] "black" $OriginPointSize;

make_message;

pack $MenuBar $Canvas \
	-side top \
	-fill x;

pack $Label   \
	-side bottom \
	-fill x;

if { ! $IsApplet } {
	wm deiconify .
}

update idletasks;

proc iamneverevercalledandifiamitisprobablyabigmistake {} {

# following is just data for reading and sending to uudecode.
# don't know what to do on windows or mac. Probably have to live
# with 2nd file in the install directory.
	
set data {
BEGIN_UU
begin 644 mstp.gif
M1TE&.#=AP`-8`N<`````````````````````````````````````````````
M`````````````````````/___^#BXL'%QJ.HJ82+C65N<$=15"@T-PH8&Q`Q
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