FractaSketch: a tool for exploring fractal geometry by Peter Van Roy FractaSketch is a Macintosh program that allows students, mathematicians, graphic artists, and curious people to rapidly design and draw shapes of great intricacy. The figures range from symmetric and regular structures to patterns that seem completely random. The figures are actually fractals, shapes described by a dimension that need not be a whole number. This sets them apart from shapes in traditional Euclidean geometry such as points, lines, and planes, which have dimensions of 0, 1, and 2 respectively. A fractal with a dimension between 1 and 2 is intermediate between a line and a plane. It is more than a line (it has infinite length) and less than a plane (it has zero area). When its dimension gets closer to 2 the shape tends to fill the plane more and more. All fractals created by FractaSketch are made of many small replicas of themselves, i.e. they are self-similar in mathematicians' jargon. An example of this is the Koch snowflake, which has a dimension of 1.26: It is made of four smaller copies of itself: copy 2 copy 3 copy 1 copy 4 The program calculates the dimension of a fractal exactly. A fractal can be saved to a file in a compact form, or printed in high resolution. Since fractals are complex figures, care has been taken to ensure that no detail is lost when transferring a picture through the clipboard or when printing. The drawing algorithms have been optimized for the greatest drawing speed. The mathematics underlying fractal geometry was developed near the turn of the century, and has remained relatively unknown until recently. The recent blossoming of the field is fueled partly by the ability to make pictures of these complex shapes, and partly by the realization that the world around us is filled with irregular shapes that are actually fractals. The first views of these shapes were provided by Benoît Mandelbrot in his book “Fractals: Form, Chance and Dimension”. Since then many isolated views have been made, mostly by solitary explorers armed with massive computing power. FractaSketch was developed to allow everyone to be an explorer. It runs well on a Macintosh with 512K of memory. Creating a fractal in FractaSketch consists of two parts: First you create a template, which is a shape that is the heart of the fractal. Then you choose the drawing commands that draw this shape in the desired manner. All of this is done graphically and quickly. A template consists of a series of line segments that is entered with the mouse. A complex shape can be the result of a simple template. For example, the template below: is the basis of the following intricate drawing (of dimension 1.75): Many objects in the world around us are fract…

Fractal! version 1.4 A program for generating Fractal landscapes. by Ed Rotberg -1- Table of Contents Introduction..............................................................................................3 The File Menu..........................................................................................4 Open ................................................................................................4 Save.................................................................................................4 Save As...........................................................................................5 Save PICT File...............................................................................5 Save PICT File As.........................................................................5 Save QT Compressed PICT.........................................................5 Open Grid File...............................................................................6 Close Grid File...............................................................................7 Script ...............................................................................................7 Export............................................................................................10 Quit ...............................................................................................10 The Edit Menu........................................................................................11 Defaults.........................................................................................11 The Subdivides Menu ..........................................................................13 The Appearance Menu.........................................................................15 Fixed Seed ....................................................................................15 Lines..............................................................................................16 Polygons .......................................................................................16 Noise Type ...................................................................................16 Alternate View............................................................................17 Modify Parameters.....................................................................18 Levels............................................................................................19 Color..............................................................................................22 Fog Color.............................................................................22 Water Color.................................................................…

FS 2.0 manual 2022/09/18, 02:58 The Guide to Drawing with FractaSketch 2.0 (draft) Marie-Therese Van Roy Manual of FractaSketch version 2.0 Copyright © 1997 Marie-Therese Van Roy and Dynamic Software Table of Contents Introduction 1 Chapter 1. Creating a New Design 2 A The Template 2 https://www.info.ucl.ac.be/~pvr/FractaManual/index.html Page 1 of 37 FS 2.0 manual 2022/09/18, 02:58 The Palette of Line Types 4 B Drawing the Fractal 5 C Editing the Template 6 Chapter 2. Basic Patterns 8 A Plant Patterns 8 The Tree (Figs. 7 & 8) 8 The Fern (Figs. 9 & 10) 10 B Geometrical Patterns 11 The Spiral (Fig. 11) 11 The Square Tiling (Fig. 12) 12 The Hexagonal Tiling (Fig. 13) 12 The Square (Fig. 14) 13 C Decorative Patterns 13 The Dragon (Fig. 15) 13 The Filled Snowflake (Fig. 16) 14 Chapter 3. Color 15 A The Color Triangle 15 The Grayscale Bar 17 Tuning the Colorization 17 B Monochrome and Bichrome Coloring 18 C Background Color 18 D Spill 18 Chapter 4. Associations 20 A The Process 20 B Using Arbitrary Shapes 24 C Several Designs side by side 24 Chapter 5. Additional Commands 26 https://www.info.ucl.ac.be/~pvr/FractaManual/index.html Page 2 of 37 FS 2.0 manual 2022/09/18, 02:58 A Simple Commands 26 B Complex Commands 27 Precision Display 27 Multiple Windows with Automatic Links 28 Double Linking 28 Chapter 6. Command Reference 29 File 29 Edit 30 Grid 31 Color 32 Spill 33 …

Fracture User Manual Last modified November 1, 2003. By Ben Haller. Copyright © 2003 Stick Software. [ This manual is only available in English at present. ] Fracture is a beautiful fractal screensaver for Mac OS X. This manual assumes that you have already downloaded a copy of Fracture; if not, visit Fracture's main page at http://www.sticksoftware.com/software/Fracture.html. It also assumes that you know all the basics of using the Macintosh in Mac OS X, including using the mouse, menus, and windows, and opening and saving files. Right now this "manual" is really an FAQ (frequently asked questions) list, because Fracture is simple enough that it doesn't seem to merit a full manual — that would just be a lot of work and would probably be less effective at answering actual user questions. Let us know if you disagree, however; if a full manual is needed for Fracture, it can be made. Please send comments on this manual to us at support@sticksoftware.com. Thanks! Questions What is Fracture and what does it do, in a nutshell? How do I install Fracture? How do I make Fracture run as my screensaver? How do I configure Fracture? What are all these weird controls? ("Fractals" tab) What are all these weird controls? ("Display" tab) What are all these weird controls? ("Saving" tab) What are all these weird controls? ("Registration" tab) How do I control Fracture while it is running? What do I do with these .fracture files? What bugs and issues are known for Fracture? What is shareware? How do I pay? What is Fracture and what does it do, in a nutshell? Fracture is a beautiful fractal screensaver for Mac OS X. It's not really important for understanding Fracture, but a fractal is a mathematical entity that exhibits characteristics of self-similarity and complexity at arbitrary levels of magnification. Or something along those lines; I don't know whether a strict definition of what is and is not a fractal has really been arrived at. You know one when you see one!!:->. The point, here, is that fractals are beautiful. Fracture can create images like this: Lots of images created by Fracture can be found at our gallery at http://www.sticksoftware.com/gallery.html; making your own is as simple as installing Fracture and letting it run for a little while! For more basic information on Fracture, please see its home page at http://www.sticksoftware.com/software/Fracture.html. How do I install Fracture? Screensavers can live in a few standard locations in OS X. The screensaver engine expects to find them in those locations, and so only those locations will work. For our purposes here, there are two that matter: /Library/Screen Savers/, and ~/Library/Screen Savers/ ("~" being short for the location of your home directory). To install Fracture, you copy it to one of these folders. And that's it. Which folder should you use? That depends upon whether or not you have Administrator privileges on your machine, and on whether you want Fracture to be visibl…

MACINTOSH QUESTIONS AND ANSWERS This document was designed and produced using FrameMaker 3.0. Frame Valen document publishing softwere MAC-514 TABLE OF CONTENTS Z . TARGET CUSTOMERS What is the audience for FrameMaker on the Macintosh and what . e application is FrameMaker best suited for? ........0...2.....-4 6 . Who are the users that Frame is not largeting with this product? . ..6 WHAT'S NEW IN How does FrameMaker differ from previous releases? .......0.... 7 Is there anything else that makes FrameMaker 3.0 special FRAMEMAKER 3.0? orunusual? oo... 0.000 eeeeee eee eee 7 e Are there any other enhancements of interest lo existing . FrameMaker users? 2.0.00... 00. c cece ee eee ee eens 7 e Is FrameMaker 3.0 a new release or just an upgrade to . FrameMaker 2.1? 0.00... cece ene eee 7 How do FrameMaker tables differ from the competition? ......... 8 . + What is conditional text? 2.00.00 eee eee 9 What are the end-user benefits of conditional text? ............ 9 * . Why should I pay for a feature like conditional text when [ don’t have any use for it? 2.200000... eee eee eee eee 9 . Can FrameMaker 2.1 users share files across platforms with FrameMaker 3.0 users? . 0.00.20. 0 cee eee ences 9 What are the hardware and software requirements for FrameMaker 3.0? 20.0... 220 ce ee eee eee 10 How can users upgrade their FrameMaker 2.1 to FrameMaker 3.0? 0.0.02. 0 cece ce c eee eee ees 10 How does FrameMaker 3.0 on the Macintosh differ from conventional desktop publishing? .............0...00 2c eee ee 10 HARDWARE AND What are the hardware and software requirements for SOFTWARE COMPATIBILITY FrameMaker on the Macintosh? .......000 000002200 eee ee eee fl …

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