Jump to content

Search the Community

Showing results for tags 'iterate'.

  • Search By Tags

    Type tags separated by commas.
  • Search By Author

Content Type


  • CADTutor
    • News, Announcements & FAQ
    • Feedback
  • AutoCAD
    • AutoCAD Beginners' Area
    • AutoCAD 2D Drafting, Object Properties & Interface
    • AutoCAD Drawing Management & Output
    • AutoCAD 3D Modelling & Rendering
    • AutoCAD Vertical Products
    • AutoCAD LT
    • CAD Management
    • AutoCAD Bugs, Error Messages & Quirks
    • AutoCAD General
    • AutoCAD Blogs
  • AutoCAD Customization
    • The CUI, Hatches, Linetypes, Scripts & Macros
    • AutoLISP, Visual LISP & DCL
    • .NET, ObjectARX & VBA
    • Application Beta Testing
    • Application Archive
  • Other Autodesk Products
    • Autodesk 3ds Max
    • Autodesk Revit
    • Autodesk Inventor
    • Autodesk Software General
  • Other CAD Products
    • BricsCAD
    • SketchUp
    • Rhino
    • SolidWorks
    • MicroStation
    • Design Software
    • Catch All
  • Resources
    • Tutorials & Tips'n'Tricks
    • AutoCAD Museum
    • Blocks, Images, Models & Materials
    • Useful Links
  • Community
    • Introduce Yourself
    • Showcase
    • Work In Progress
    • Jobs & Training
    • Chat
    • Competitions


  • Programs and Scripts
  • 2D AutoCAD Blocks
  • 3D AutoCAD Blocks
  • Images
    • Backgrounds

Find results in...

Find results that contain...

Date Created

  • Start


Last Updated

  • Start


Filter by number of...

Found 1 result

  1. As many of you will know, I am currently studying for a degree in Mathematics, and, as part of the course, we study the dynamics of such functions as the Logistic Map. I've always been fascinated by this ostensibly simple map, which produces astoundingly complex dynamics resulting in chaos if a single parameter is varied. Quick Overview of the Logistic Map The Logistic map was originally devised as a population model, to measure the growth of a population, noting that the rate of reproduction of a species is proportional to the existing population and restricted by the available resources and competition for such resoures. We are iterating the difference equation: x[n+1] = rx[n](1-x[n]) For varying values of 0 Function maximum occurs at r/4, hence for 0 For 0 For 1 As r approaches 3, convergence to the fixed point x=r-1/r becomes increasingly slow, and a periodic point of period 2 appears when 3 From here we have a period-doubling cascade with the period doubling at a rate of approximately 4.669 (the Feigenbaum Constant). For r > 3.57 chaos emerges, with 'islands of stability' for various values of r at which periods of order 5,6,7 emerge. For r=4 the interval [0,1] is mapped to a set resembling a Cantor Set, with Hausdorff Dimension of about 0.538. A Visual Study of the Logistic Map To view the general dynamics of the Logistic Map, I have created a program where the parameter 'r' and the initial state 'x' can be varied, and the long-term behaviour of the model is displayed. To run the program: Download the attached Logistic.lsp and Logistic.dcl files. Ensure the Logistic.dcl file is located in an AutoCAD Support Path. Load the Logistic.lsp like any other LISP program (for instructions on how to do this, see here). Run the program by typing 'Logistic' at the AutoCAD command-line. I hope that I have sparked some interest in this area of mathematics and look forward to discussing the subject with the community. Enjoy! Lee logistic.lsp logistic.dcl
  • Create New...