Macdraw Replacement
2021年11月4日Download here: http://gg.gg/wgh8x
Resize by 50%? It’s probably just high MP from your camera. If that doesn’t go far enough then save them as jpg instead of png. It’s not like high quality’s really all that necessary for what people are looking for to help out with suggestions.
*Macdraw Replacement Blades
*Macdraw Replacement Cushions
*Macdraw Replacement Filters
*Macdraw Replacement Windows
*Macdraw Replacement
MacDraft Alternatives. MacDraft is described as ’Professional, powerful 2D CAD, drafting, technical illustration, architectural drawing and more in one easy-to-use, CAD software package’ and is an app in the Photos & Graphics category. Apr 14, 2014 MacDraw (Mac abandonware from 1984) To date, Macintosh Repository served 1455942 old Mac files, totaling more than 290530.5GB!Resize by 50% using what image manipulation program that comes standard with Mac OS X 10.10? When you open the images on your mac, don’t they open in Preview by default? If so, Tools... Adjust Size (at least that’s the menu option in 10.12; it might be Tools... Resize in 10.10?). Also, File... Export... will let you convert if the images aren’t already JPG(Lindenmayer Systems)Written by Paul BourkeVersion 2.5, July 1991
IntroductionThis program implements some of the L-Systems discussed in ’Lecture Notes inBiomathematics’ by Przemyslaw Prusinkiewcz and James Hanan. A brief descriptionof an 0L system will be presented here but for a more complete description theuser should consult the literature.The application was initially written to investigate methods of incorporatingobjects with a large number of drawing elements (lines, polygons) into a CADpackage. L Systems is one way for example of ’generating’ trees at therendering stage but not during the editing stage where the image complexitywill slow down the response time.Simple example of a 0L systemA string of characters (symbols) is rewritten on each iteration according tosome replacement rules. Consider an initial string (axiom)F+F+F+F
and a rewriting rule F --> F+F-F-FF+F+F-F
After one iteration the following string would resultF+F-F-FF+F+F-F + F+F-F-FF+F+F-F + F+F-F-FF+F+F-F + F+F-F-FF+F+F-FFor the next iteration the same rule is applied but now to the string resultingfrom the last iterationF+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-FF+F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-F+ F+F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-FF+ F-F-FF+F+ F-F+ F+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+F-F+ F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-FF+ F-F-FF+ F+ F-F+ F+F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F+ F+F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-FF+ F-F-FF+ F+ F-F+ F+ F-F-FF+F+ F-F+ F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-FSome symbols are now given a graphical meaning, for example, F means moveforward drawing a line, + means turn right by some predefined angle (90 degreesin this case), - means turn left.Using these symbols the initial string F+F+F+F is just a rectangle (ø =90). The replacement rule F --> F+F-F-FF+F+F-F replaces each forwardmovement by the following figureThe first iteration interpreted graphically isThe next iteration interpreted graphically is:
and so on.Example:
Axiom XF --> FFX --> F-[[X]+X]+F[+FX]-Xø = 22.5Example:
Axiom F+F+F+FF --> FF+F-F+F+FFø = 90SymbolsThe following characters have a geometric interpretation.When drawing the graphical representation of the L string all other charactersare ignored.The user may choose and use any other single printable characters for thereplacement rules except, note: this excludes ’white’ characters such as spacesand tabs. For context sensitive L systems the * character is used to representany match.See the SYMBOL menu item for a summary of the reserved symbols.MenusAswith most applications the ABOUT menu item located in the Apple menu before thedesk accessories displays information such as the version number and contactaddress of the developer.Thisis the standard FILE menu although some of the items are not implemented.
NEW resets all the variables including the rules to their default values.
OPEN to load a rule description file previously saved or possibly created witha text editor.SAVE and SAVE AS create rule description files.
PRINT and PAGESETUP control direct printing.
QUIT to exit from the program when finished.The standard EDIT menu. The first 5 items are only included for compatibilityreasons and do not apply to this application. (they are used with deskaccessories in some cases)The two special copy items allow images to be transferred to other applicationsdepending on the preferred data type. Line drawings should be copied for CADpackages and bitmaps for painting programs.Normally images will be scaled to fit the window, it is possible to zoom in orout of areas with the last two items.This is the main menu for this application.REDRAW updates the current display, for example, if the drawing was cancelledwith clover-. (period)Menu items 2 through 4 control the iteration depth. RESET sets it to 0, thenumber of iterations to compute may be incremented, decremented, or set to anyparticular number.FRAME, FILL and BACKGROUND are pop-up menus that allow the colour of the lines,polygon fills and background to be set.PRODUCTIONS allows the current rules to be altered. AXIOM menu item sets theinitial string. STATE menu item varies environment variables. SYMBOL LISTdisplays the meaning given to various predefined and reserved symbols.The type of system is selectable from the last 3 items.Thiscontains a number of predefined image specifications grouped together incategories given by the pop-up menu names. Users are encouraged to submit further examples that can be added to thislibrary.
Advanced features/comments
*Always ensure that the ’[’ and ’]’ brackets match in number, ie: thereshould always be the same number of each type. If not a stack overflow willquickly occur, a message displayed, and the iteration depth decremented. Note:non matching brackets are not tested before the string in interpreted, aproblem only occurs when a stack overflow situation is encountered.
*Polygons (using ’{’ and ’}’) cannot be nested, ie: there can only be oneopen at a time. If a polygon open symbol ’{’ is encountered while anotherpolygon is still open it will be ignored. If a polygon is left open when theend of the string is reached it will be automatically closed.
*For a complete list of predefined symbol meanings look at the SYMBOL listunder the ACTION menu.
*Best quality hardcopy line drawing images can be obtained by usingMacDraw or Claris CAD. In both cases copy the image as a line drawing, paste itinto MacDraw say, set the lines to black and line width 0.1mm, then print on aLaserWriter. Note: the number of lines can quickly approach the thousands andeven tens of thousands, don’t expect the printing to be fast.
*Time consuming drawing may be cancelled by typing clover-. (period)
*The maximum length of the strings generated is 300,000 symbols.Attempting to exceed this will give an error message and automatic decrementingof the iteration count.
*The maximum stack depth is 100. This means that a bracketed string cannothave brackets nested more than 100 deep. ie: [ [ [ ] ] [ [ [ [ ] ] [ ] ] ] ]
1 2 3 2 1 2 3 4 5 4 3 4 3 2 1 0 is nested 5 deepIf the maximum stack depth is exceeded an appropriate error message will bedisplayed and the iteration depth decremented until the stack no longeroverflows.
*When copying to the clipboard as lines make the drawing window as largeas possible for maximum resolution.References
Heinz-Otto and Deitmar Saupe.The Science of Fractal Images.Springer-Verlag
Przemyslaw Prusinkiewicz.Application of L-Systems to Computer Imagery.Lecture Notes in Computer Science #291, Pages 534-548
Przemyslaw Prusinkiewicz, James Hanan.Lecture Notes in Biomathematics #79
Prusinkiewicz, P.Graphical Applications of L-Systems.Proc. of Graphics Interface 1986 - Vision Interface, 1986, Pages 247-253.
Smith, A.R.Plants, Fractals, and Formal Languages.Computer Graphics, 18, 3, 1984, Pages 1-10
Prusinkiewicz, P and Lindenmayer A.The Algorithmic Beauty of Plants.Springer Verleg, 1990, Pages 40-50
Written by Paul Bourke
axiom = aF -> >F<a -> F[+x]Fbb -> F[-y]Fax -> ay -> bangle = 45length factor = 1.36
Written by Paul Bourke
axiom = YX -> X[-FFF][+FFF]FXY -> YFX[+Y][-Y]angle = 25.7
axiom = FF -> FF+[+F-F-F]-[-F+F+F]angle = 22.5
axiom = FF -> F[+FF][-FF]F[-F][+F]Fangle = 35
Attributed to Saupe
axiom = VZFFFV -> [+++W][---W]YVW -> +X[-W]ZX -> -W[+X]ZY -> YZZ -> [-FFF][+FFF]Fangle = 20
axiom = FXX -> >[-FX]+FXangle = 40
Written by Paul Bourke
axiom = XF -> FFX -> F[+X]F[-X]+Xangle = 20
Written by Paul Bourke
axiom = aFa -> FFFFFv[+++h][---q]fbb -> FFFFFv[+++h][---q]fcc -> FFFFFv[+++fa]fdd -> FFFFFv[+++h][---q]fee -> FFFFFv[+++h][---q]fgg -> FFFFFv[---fa]fah -> ifFFi -> fFFF[--m]jj -> fFFF[--n]kk -> fFFF[--o]ll -> fFFF[--p]m -> fFnn -> fFoo -> fFpp -> fFq -> rfFr -> fFFF[++m]ss -> fFFF[++n]tt -> fFFF[++o]uu -> fFFF[++p]v -> Fvangle = 12
axiom = aFa -> FFFFFy[++++n][----t]fbb -> +FFFFFy[++++n][----t]fcc -> FFFFFy[++++n][----t]fdd -> -FFFFFy[++++n][----t]fee -> FFFFFy[++++n][----t]fgg -> FFFFFy[+++fa]fhh -> FFFFFy[++++n][----t]fii -> +FFFFFy[++++n][----t]fjj -> FFFFFy[++++n][----t]fkk -> -FFFFFy[++++n][----t]fll -> FFFFFy[++++n][----t]fmm -> FFFFFy[---fa]fan -> ofFFFo -> fFFFpp -> fFFF[-s]qq -> fFFF[-s]rr -> fFFF[-s]s -> fFfFt -> ufFFFu -> fFFFvv -> fFFF[+s]ww -> fFFF[+s]xx -> fFFF[+s]y -> Fyangle = 12
Written by Paul Bourke
axiom = FF -> FF-[XY]+[XY]X -> +FYY -> -FXangle = 22.5
Written by Paul BourkeJuly 1990
L-Systems
axiom = F+F+FF -> F-F+Fangle = 120
As an IFS
The IFS equations are as followsxn+1 = a xn + b yn + e
yn+1 = c xn + d yn + fThe parameter table:
Written by Paul BourkeJune 1990Attributed to Dekking, 1982
axiom = -YFX -> XFX-YF-YF+FX+FX-YF-YFFX+YF+FXFXYF-FX+YF+FXFX+YF-FXYF-YF-FX+FX+YFYF-Y -> +FXFX-YF-YF+FX+FXYF+FX-YFYF-FX-YF+FXYFYF-FX-YFFX+FX+YF-YF-FX+FX+YFYangle = 90
Written by Paul BourkeAugust 1990First reported circa 1912
axiom = F+XF+F+XFX -> XF-F+F-XF+F+XF-F+F-Xangle = 90
Written by Paul BourkeJune 1990
axiom = F+F+F+FF -> FF+F++F+Fangle = 90
Derby, Western Australia
Written by Paul BourkeJune 1990First documented circa 1890
axiom = XX -> XFYFX+F+YFXFY-F-XFYFXY -> YFXFY-F-XFYFX+F+YFXFYangle = 90
Written by Paul BourkeJuly 1990
axiom = FF -> F-F+F+F-Fangle = 90
Variation by Hasan Hosam.December 2018axiom = FF+FF+FF+FFF -> F+F-F-F+Fangle = 90
Written by Paul BourkeJuly 1990
axiom = F+F+F+FF -> F+F-F-FFF+F+F-Fangle = 90String length: 63
String length: 567
String length: 5103
String length: 45927
axiom = F+F+F+FF -> F-FF+FF+F+F-F-FF+F+F-F-FF-FF+Fangle = 90
Variation by Hasan Hosam.December 2018axiom = X+X+X+X+X+X+X+XX -> X+YF++YF-FX--FXFX-YF+XY -> -FX+YFYF++YF+FX--FX-YFangle = 45
Written by Paul BourkeJune 1990Fractal Dimension: 1.5
axiom = F+F+F+FF -> F+F-F-FF+F+F-Fangle = 90
Written by Paul BourkeJune 1990
axiom = F+F+F+FF -> FF+F+F+F+FFangle = 90
Written by Paul BourkeJune 1990Attributed to the German mathematician David Hilbert, circa 1891
axiom = XX -> -YF+XFX+FY-Y -> +XF-YFY-FX+angle = 90
Written by Paul BourkeJune 1990
axiom = YFX -> YF+XF+YY -> XF-YF-Xangle = 60
YF+XF+YF-XF-YF-XF-YF+XF+YFXF-YF-XF+YF+XF+YF+XF-YF-XF-YF+XF+YF-XF-YF-XF-YF+XF+YF-XF-YF-XF+YF+XF+YF+XF-YF-XFYF+XF+YF-XF-YF-XF-YF+XF+YF+XF-YF-XF+YF+XF+YF+XF-YF-XF+YF+XF+YF-XF-YF-XF-YF+XF+YF-XF-YF-XF+YF+XF+YF+XF-YF-XF-YF+XF+YF-XF-YF-XF-YF+XF+YF-XF-YF-XF+YF+XF+YF+XF-YF-XF-YF+XF+YF-XF-YF-XF-YF+XF+YF+XF-YF-XF+YF+XF+YF+XF-YF-XF+YF+XF+YF-XF-YF-XF-YF+XF+YFXF-YF-XF+YF+XF+YF+XF-YF-XF-YF+XF+YF-XF-YF-XF-YF+XF+YF-XF-YF-XF+YF+XF+YF+XF-YF-XF+YF+XF+YF-XF-YF-XF-YF+XF+YF+XF-YF-XF+YF+XF+YF+XF-YF-XF+YF+XF+YF-XF-YF-XF-YF+XF+YF+XF-YF-XF+YF+XF+YF+XF-YF-XF-YF+XF+YF-XF-YF-XF-YF+XF+YF-XF-YF-XF+YF+XF+YF+XF-YF-XF-YF+XF+YF-XF-YF-XF-YF+XF+YF+XF-YF-XF+YF+XF+YF+XF-YF-XF+YF+XF+YF-XF-YF-XF-YF+XF+YF-XF-YF-XF+YF+XF+YF+XF-YF-XF-YF+XF+YF-XF-YF-XF-YF+XF+YF-XF-YF-XF+YF+XF+YF+XF-YF-XF-YF+XF+YF-XF-YF-XF-YF+XF+YF+XF-YF-XF+YF+XF+YF+XF-YF-XF+YF+XF+YF-XF-YF-XF-YF+XF+YF-XF-YF-XF+YF+XF+YF+XF-YF-XF-YF+XF+YF-XF-YF-XF-YF+XF+YF-XF-YF-XF+YF+XF+YF+XF-YF-XF+YF+XF+YF-XF-YF-XF-YF+XF+YF+XF-YF-XF+YF+XF+YF+XF-YF-XF+YF+XF+YF-XF-YF-XF-YF+XF+YF+XF-YF-XF+YF+XF+YF+XF-YF-XF-YF+XF+YF-XF-YF-XF-YF+XF+YF-XF-YF-XF+YF+XF+YF+XF-YF-XFString length: 2186String length: 6560
Written by Paul BourkeJune 1990Fractal Dimension: log(4)/log(3) = 1.262
L-Systems
axiom = F++F++FF -> F-F++F-Fangle = 60
IFS
The IFS equations are as followsxn+1 = a xn + b yn + e
yn+1 = c xn + d yn + fThe parameter table:
Written by Paul BourkeJune 1990
axiom = F+F+F+FF -> F+FF++F+Fangle = 90
Written by Paul BourkeAugust 1990
axiom = F+F+F+FF -> F+F-F+F+Fangle = 90
Written by Paul BourkeSeptember 1990
axiom = F++F++F++F++FF -> F++F++F|F-F++Fangle = 36
Written by Paul BourkeJune 1990Fractal Dimension: log(7)/log(3) = 1.771
axiom = F+F+F+FF -> FF+F-F+F+FFangle = 90
Written by Paul BourkeJune 1990
axiom = F+F+F+FF -> FF+F+F+F+F+F-Fangle = 90
Written by Paul BourkeAugust 1990Attributed to David and Knuth, 1970
Macdraw Replacement Blades
axiom = FXX -> X+YF+Y -> -FX-Yangle = 90
Written by Paul BourkeJuly 1990Attributed to Mandelbrot, 1982Macdraw Replacement Cushions
axiom = XFX -> X+YF++YF-FX--FXFX-YF+Y -> -FX+YFYF++YF+FX--FX-Yangle = 60
Written by Paul BourkeFebruary 2019
axiom = FF -> -F++F-angle = 45
Written by Paul BourkeRules by Chris WallaceNovember 2019
axiom = F--XF--F--XFX -> XF+F+XF--F--XF+F+Xangle = 45
Written by Paul Bourke
axiom = -X--XX -> XFX--XFXangle = 45
Written by Paul Bourke
axiom = Y---YX -> {F-F}{F-F}--[--X]{F-F}{F-F}--{F-F}{F-F}--Y -> f-F+X+F-fYangle = 60
Written by Paul Bourke
axiom = F+XF+F+XFX -> X{F-F-F}+XF+F+X{F-F-F}+Xangle = 90
January 2019
axiom = (-D--D)A -> F++FFFF--F--FFFF++F++FFFF--FB -> F--FFFF++F++FFFF--F--FFFF++FC -> BFA--BFAD -> CFC--CFCangle = 45Macdraw Replacement FiltersMacdraw Replacement WindowsKolams from IndiaMacdraw ReplacementKolam patterns from the South of India, drawn by rice powder in front ofhouses every morning before the doorway is used.
Download here: http://gg.gg/wgh8x
https://diarynote-jp.indered.space
Resize by 50%? It’s probably just high MP from your camera. If that doesn’t go far enough then save them as jpg instead of png. It’s not like high quality’s really all that necessary for what people are looking for to help out with suggestions.
*Macdraw Replacement Blades
*Macdraw Replacement Cushions
*Macdraw Replacement Filters
*Macdraw Replacement Windows
*Macdraw Replacement
MacDraft Alternatives. MacDraft is described as ’Professional, powerful 2D CAD, drafting, technical illustration, architectural drawing and more in one easy-to-use, CAD software package’ and is an app in the Photos & Graphics category. Apr 14, 2014 MacDraw (Mac abandonware from 1984) To date, Macintosh Repository served 1455942 old Mac files, totaling more than 290530.5GB!Resize by 50% using what image manipulation program that comes standard with Mac OS X 10.10? When you open the images on your mac, don’t they open in Preview by default? If so, Tools... Adjust Size (at least that’s the menu option in 10.12; it might be Tools... Resize in 10.10?). Also, File... Export... will let you convert if the images aren’t already JPG(Lindenmayer Systems)Written by Paul BourkeVersion 2.5, July 1991
IntroductionThis program implements some of the L-Systems discussed in ’Lecture Notes inBiomathematics’ by Przemyslaw Prusinkiewcz and James Hanan. A brief descriptionof an 0L system will be presented here but for a more complete description theuser should consult the literature.The application was initially written to investigate methods of incorporatingobjects with a large number of drawing elements (lines, polygons) into a CADpackage. L Systems is one way for example of ’generating’ trees at therendering stage but not during the editing stage where the image complexitywill slow down the response time.Simple example of a 0L systemA string of characters (symbols) is rewritten on each iteration according tosome replacement rules. Consider an initial string (axiom)F+F+F+F
and a rewriting rule F --> F+F-F-FF+F+F-F
After one iteration the following string would resultF+F-F-FF+F+F-F + F+F-F-FF+F+F-F + F+F-F-FF+F+F-F + F+F-F-FF+F+F-FFor the next iteration the same rule is applied but now to the string resultingfrom the last iterationF+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-FF+F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-F+ F+F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-FF+ F-F-FF+F+ F-F+ F+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+F-F+ F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-FF+ F-F-FF+ F+ F-F+ F+F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F+ F+F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-FF+ F-F-FF+ F+ F-F+ F+ F-F-FF+F+ F-F+ F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-FSome symbols are now given a graphical meaning, for example, F means moveforward drawing a line, + means turn right by some predefined angle (90 degreesin this case), - means turn left.Using these symbols the initial string F+F+F+F is just a rectangle (ø =90). The replacement rule F --> F+F-F-FF+F+F-F replaces each forwardmovement by the following figureThe first iteration interpreted graphically isThe next iteration interpreted graphically is:
and so on.Example:
Axiom XF --> FFX --> F-[[X]+X]+F[+FX]-Xø = 22.5Example:
Axiom F+F+F+FF --> FF+F-F+F+FFø = 90SymbolsThe following characters have a geometric interpretation.When drawing the graphical representation of the L string all other charactersare ignored.The user may choose and use any other single printable characters for thereplacement rules except, note: this excludes ’white’ characters such as spacesand tabs. For context sensitive L systems the * character is used to representany match.See the SYMBOL menu item for a summary of the reserved symbols.MenusAswith most applications the ABOUT menu item located in the Apple menu before thedesk accessories displays information such as the version number and contactaddress of the developer.Thisis the standard FILE menu although some of the items are not implemented.
NEW resets all the variables including the rules to their default values.
OPEN to load a rule description file previously saved or possibly created witha text editor.SAVE and SAVE AS create rule description files.
PRINT and PAGESETUP control direct printing.
QUIT to exit from the program when finished.The standard EDIT menu. The first 5 items are only included for compatibilityreasons and do not apply to this application. (they are used with deskaccessories in some cases)The two special copy items allow images to be transferred to other applicationsdepending on the preferred data type. Line drawings should be copied for CADpackages and bitmaps for painting programs.Normally images will be scaled to fit the window, it is possible to zoom in orout of areas with the last two items.This is the main menu for this application.REDRAW updates the current display, for example, if the drawing was cancelledwith clover-. (period)Menu items 2 through 4 control the iteration depth. RESET sets it to 0, thenumber of iterations to compute may be incremented, decremented, or set to anyparticular number.FRAME, FILL and BACKGROUND are pop-up menus that allow the colour of the lines,polygon fills and background to be set.PRODUCTIONS allows the current rules to be altered. AXIOM menu item sets theinitial string. STATE menu item varies environment variables. SYMBOL LISTdisplays the meaning given to various predefined and reserved symbols.The type of system is selectable from the last 3 items.Thiscontains a number of predefined image specifications grouped together incategories given by the pop-up menu names. Users are encouraged to submit further examples that can be added to thislibrary.
Advanced features/comments
*Always ensure that the ’[’ and ’]’ brackets match in number, ie: thereshould always be the same number of each type. If not a stack overflow willquickly occur, a message displayed, and the iteration depth decremented. Note:non matching brackets are not tested before the string in interpreted, aproblem only occurs when a stack overflow situation is encountered.
*Polygons (using ’{’ and ’}’) cannot be nested, ie: there can only be oneopen at a time. If a polygon open symbol ’{’ is encountered while anotherpolygon is still open it will be ignored. If a polygon is left open when theend of the string is reached it will be automatically closed.
*For a complete list of predefined symbol meanings look at the SYMBOL listunder the ACTION menu.
*Best quality hardcopy line drawing images can be obtained by usingMacDraw or Claris CAD. In both cases copy the image as a line drawing, paste itinto MacDraw say, set the lines to black and line width 0.1mm, then print on aLaserWriter. Note: the number of lines can quickly approach the thousands andeven tens of thousands, don’t expect the printing to be fast.
*Time consuming drawing may be cancelled by typing clover-. (period)
*The maximum length of the strings generated is 300,000 symbols.Attempting to exceed this will give an error message and automatic decrementingof the iteration count.
*The maximum stack depth is 100. This means that a bracketed string cannothave brackets nested more than 100 deep. ie: [ [ [ ] ] [ [ [ [ ] ] [ ] ] ] ]
1 2 3 2 1 2 3 4 5 4 3 4 3 2 1 0 is nested 5 deepIf the maximum stack depth is exceeded an appropriate error message will bedisplayed and the iteration depth decremented until the stack no longeroverflows.
*When copying to the clipboard as lines make the drawing window as largeas possible for maximum resolution.References
Heinz-Otto and Deitmar Saupe.The Science of Fractal Images.Springer-Verlag
Przemyslaw Prusinkiewicz.Application of L-Systems to Computer Imagery.Lecture Notes in Computer Science #291, Pages 534-548
Przemyslaw Prusinkiewicz, James Hanan.Lecture Notes in Biomathematics #79
Prusinkiewicz, P.Graphical Applications of L-Systems.Proc. of Graphics Interface 1986 - Vision Interface, 1986, Pages 247-253.
Smith, A.R.Plants, Fractals, and Formal Languages.Computer Graphics, 18, 3, 1984, Pages 1-10
Prusinkiewicz, P and Lindenmayer A.The Algorithmic Beauty of Plants.Springer Verleg, 1990, Pages 40-50
Written by Paul Bourke
axiom = aF -> >F<a -> F[+x]Fbb -> F[-y]Fax -> ay -> bangle = 45length factor = 1.36
Written by Paul Bourke
axiom = YX -> X[-FFF][+FFF]FXY -> YFX[+Y][-Y]angle = 25.7
axiom = FF -> FF+[+F-F-F]-[-F+F+F]angle = 22.5
axiom = FF -> F[+FF][-FF]F[-F][+F]Fangle = 35
Attributed to Saupe
axiom = VZFFFV -> [+++W][---W]YVW -> +X[-W]ZX -> -W[+X]ZY -> YZZ -> [-FFF][+FFF]Fangle = 20
axiom = FXX -> >[-FX]+FXangle = 40
Written by Paul Bourke
axiom = XF -> FFX -> F[+X]F[-X]+Xangle = 20
Written by Paul Bourke
axiom = aFa -> FFFFFv[+++h][---q]fbb -> FFFFFv[+++h][---q]fcc -> FFFFFv[+++fa]fdd -> FFFFFv[+++h][---q]fee -> FFFFFv[+++h][---q]fgg -> FFFFFv[---fa]fah -> ifFFi -> fFFF[--m]jj -> fFFF[--n]kk -> fFFF[--o]ll -> fFFF[--p]m -> fFnn -> fFoo -> fFpp -> fFq -> rfFr -> fFFF[++m]ss -> fFFF[++n]tt -> fFFF[++o]uu -> fFFF[++p]v -> Fvangle = 12
axiom = aFa -> FFFFFy[++++n][----t]fbb -> +FFFFFy[++++n][----t]fcc -> FFFFFy[++++n][----t]fdd -> -FFFFFy[++++n][----t]fee -> FFFFFy[++++n][----t]fgg -> FFFFFy[+++fa]fhh -> FFFFFy[++++n][----t]fii -> +FFFFFy[++++n][----t]fjj -> FFFFFy[++++n][----t]fkk -> -FFFFFy[++++n][----t]fll -> FFFFFy[++++n][----t]fmm -> FFFFFy[---fa]fan -> ofFFFo -> fFFFpp -> fFFF[-s]qq -> fFFF[-s]rr -> fFFF[-s]s -> fFfFt -> ufFFFu -> fFFFvv -> fFFF[+s]ww -> fFFF[+s]xx -> fFFF[+s]y -> Fyangle = 12
Written by Paul Bourke
axiom = FF -> FF-[XY]+[XY]X -> +FYY -> -FXangle = 22.5
Written by Paul BourkeJuly 1990
L-Systems
axiom = F+F+FF -> F-F+Fangle = 120
As an IFS
The IFS equations are as followsxn+1 = a xn + b yn + e
yn+1 = c xn + d yn + fThe parameter table:
Written by Paul BourkeJune 1990Attributed to Dekking, 1982
axiom = -YFX -> XFX-YF-YF+FX+FX-YF-YFFX+YF+FXFXYF-FX+YF+FXFX+YF-FXYF-YF-FX+FX+YFYF-Y -> +FXFX-YF-YF+FX+FXYF+FX-YFYF-FX-YF+FXYFYF-FX-YFFX+FX+YF-YF-FX+FX+YFYangle = 90
Written by Paul BourkeAugust 1990First reported circa 1912
axiom = F+XF+F+XFX -> XF-F+F-XF+F+XF-F+F-Xangle = 90
Written by Paul BourkeJune 1990
axiom = F+F+F+FF -> FF+F++F+Fangle = 90
Derby, Western Australia
Written by Paul BourkeJune 1990First documented circa 1890
axiom = XX -> XFYFX+F+YFXFY-F-XFYFXY -> YFXFY-F-XFYFX+F+YFXFYangle = 90
Written by Paul BourkeJuly 1990
axiom = FF -> F-F+F+F-Fangle = 90
Variation by Hasan Hosam.December 2018axiom = FF+FF+FF+FFF -> F+F-F-F+Fangle = 90
Written by Paul BourkeJuly 1990
axiom = F+F+F+FF -> F+F-F-FFF+F+F-Fangle = 90String length: 63
String length: 567
String length: 5103
String length: 45927
axiom = F+F+F+FF -> F-FF+FF+F+F-F-FF+F+F-F-FF-FF+Fangle = 90
Variation by Hasan Hosam.December 2018axiom = X+X+X+X+X+X+X+XX -> X+YF++YF-FX--FXFX-YF+XY -> -FX+YFYF++YF+FX--FX-YFangle = 45
Written by Paul BourkeJune 1990Fractal Dimension: 1.5
axiom = F+F+F+FF -> F+F-F-FF+F+F-Fangle = 90
Written by Paul BourkeJune 1990
axiom = F+F+F+FF -> FF+F+F+F+FFangle = 90
Written by Paul BourkeJune 1990Attributed to the German mathematician David Hilbert, circa 1891
axiom = XX -> -YF+XFX+FY-Y -> +XF-YFY-FX+angle = 90
Written by Paul BourkeJune 1990
axiom = YFX -> YF+XF+YY -> XF-YF-Xangle = 60
YF+XF+YF-XF-YF-XF-YF+XF+YFXF-YF-XF+YF+XF+YF+XF-YF-XF-YF+XF+YF-XF-YF-XF-YF+XF+YF-XF-YF-XF+YF+XF+YF+XF-YF-XFYF+XF+YF-XF-YF-XF-YF+XF+YF+XF-YF-XF+YF+XF+YF+XF-YF-XF+YF+XF+YF-XF-YF-XF-YF+XF+YF-XF-YF-XF+YF+XF+YF+XF-YF-XF-YF+XF+YF-XF-YF-XF-YF+XF+YF-XF-YF-XF+YF+XF+YF+XF-YF-XF-YF+XF+YF-XF-YF-XF-YF+XF+YF+XF-YF-XF+YF+XF+YF+XF-YF-XF+YF+XF+YF-XF-YF-XF-YF+XF+YFXF-YF-XF+YF+XF+YF+XF-YF-XF-YF+XF+YF-XF-YF-XF-YF+XF+YF-XF-YF-XF+YF+XF+YF+XF-YF-XF+YF+XF+YF-XF-YF-XF-YF+XF+YF+XF-YF-XF+YF+XF+YF+XF-YF-XF+YF+XF+YF-XF-YF-XF-YF+XF+YF+XF-YF-XF+YF+XF+YF+XF-YF-XF-YF+XF+YF-XF-YF-XF-YF+XF+YF-XF-YF-XF+YF+XF+YF+XF-YF-XF-YF+XF+YF-XF-YF-XF-YF+XF+YF+XF-YF-XF+YF+XF+YF+XF-YF-XF+YF+XF+YF-XF-YF-XF-YF+XF+YF-XF-YF-XF+YF+XF+YF+XF-YF-XF-YF+XF+YF-XF-YF-XF-YF+XF+YF-XF-YF-XF+YF+XF+YF+XF-YF-XF-YF+XF+YF-XF-YF-XF-YF+XF+YF+XF-YF-XF+YF+XF+YF+XF-YF-XF+YF+XF+YF-XF-YF-XF-YF+XF+YF-XF-YF-XF+YF+XF+YF+XF-YF-XF-YF+XF+YF-XF-YF-XF-YF+XF+YF-XF-YF-XF+YF+XF+YF+XF-YF-XF+YF+XF+YF-XF-YF-XF-YF+XF+YF+XF-YF-XF+YF+XF+YF+XF-YF-XF+YF+XF+YF-XF-YF-XF-YF+XF+YF+XF-YF-XF+YF+XF+YF+XF-YF-XF-YF+XF+YF-XF-YF-XF-YF+XF+YF-XF-YF-XF+YF+XF+YF+XF-YF-XFString length: 2186String length: 6560
Written by Paul BourkeJune 1990Fractal Dimension: log(4)/log(3) = 1.262
L-Systems
axiom = F++F++FF -> F-F++F-Fangle = 60
IFS
The IFS equations are as followsxn+1 = a xn + b yn + e
yn+1 = c xn + d yn + fThe parameter table:
Written by Paul BourkeJune 1990
axiom = F+F+F+FF -> F+FF++F+Fangle = 90
Written by Paul BourkeAugust 1990
axiom = F+F+F+FF -> F+F-F+F+Fangle = 90
Written by Paul BourkeSeptember 1990
axiom = F++F++F++F++FF -> F++F++F|F-F++Fangle = 36
Written by Paul BourkeJune 1990Fractal Dimension: log(7)/log(3) = 1.771
axiom = F+F+F+FF -> FF+F-F+F+FFangle = 90
Written by Paul BourkeJune 1990
axiom = F+F+F+FF -> FF+F+F+F+F+F-Fangle = 90
Written by Paul BourkeAugust 1990Attributed to David and Knuth, 1970
Macdraw Replacement Blades
axiom = FXX -> X+YF+Y -> -FX-Yangle = 90
Written by Paul BourkeJuly 1990Attributed to Mandelbrot, 1982Macdraw Replacement Cushions
axiom = XFX -> X+YF++YF-FX--FXFX-YF+Y -> -FX+YFYF++YF+FX--FX-Yangle = 60
Written by Paul BourkeFebruary 2019
axiom = FF -> -F++F-angle = 45
Written by Paul BourkeRules by Chris WallaceNovember 2019
axiom = F--XF--F--XFX -> XF+F+XF--F--XF+F+Xangle = 45
Written by Paul Bourke
axiom = -X--XX -> XFX--XFXangle = 45
Written by Paul Bourke
axiom = Y---YX -> {F-F}{F-F}--[--X]{F-F}{F-F}--{F-F}{F-F}--Y -> f-F+X+F-fYangle = 60
Written by Paul Bourke
axiom = F+XF+F+XFX -> X{F-F-F}+XF+F+X{F-F-F}+Xangle = 90
January 2019
axiom = (-D--D)A -> F++FFFF--F--FFFF++F++FFFF--FB -> F--FFFF++F++FFFF--F--FFFF++FC -> BFA--BFAD -> CFC--CFCangle = 45Macdraw Replacement FiltersMacdraw Replacement WindowsKolams from IndiaMacdraw ReplacementKolam patterns from the South of India, drawn by rice powder in front ofhouses every morning before the doorway is used.
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