END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

 Introduction: Davrin
                               October 15, 2006,
  Hi y'all

 I'm a retired pharmacist living in Melbourne, Australia

 I've been studying and researching mathematics as a passionate interest
 for the last 30 years,

 I have great interest in several disparate areas of mathematics, especially
 geometry, including Fractals, Intrinsic (Natural) Plane Geometry, Osculants &
 Glove-Osculants, and their multitudinous Orders-Of-Contact,(including their
 recursive series), Calculus of Variations in the Plane, Anallagmatic Curves
 (Self-inverters), Absolute Invariants of the General Quadratic Form in many
 planar coordinate frameworks as well as an analysis of these quadratic forms,
 Pursuit (& Pseudo-Pursuit) Curves in closed form, Fractran (al la John Horton).
 The Reciprocal System of Physical Theory (al la Dewey B. Larson), Newton's
 Equations of Motion in extended form, Gyroscopic motion,(including the actual
 spinning motion of atoms and subatomic particles), River Meander and Elastica
 Curves, Circular Asymptotes, Angle of Contingency and its many applications,
 Fractional Derivatives, Deviation (Aberration) of plane curves, Iterates and
 Semi-Iterates, Sand Dunes.

 Some of my software is Fractint for the fractals and Derive XM and Derive
 for Windows as mathematical assistants for just about any type of maths
 problem as well as plotting graphs.


 I've had a strong interest in several aspects of fractals for many years,
 back from the days of DOS, hence the use of Fractint.

 Because of the infinite variety of contrived fractals, that can be generated
 by the multitude of software around, I decided to limit my interest to
 those fractals, that can be generated solely by an input equation of a a
 plane curve.  This facility is made available by Fractint.(I don't know if
 any other software can do this, I hope that there is, since working in DOS is
 very limiting.

 This led me to discover the work of Hans Lauwerier and his partially-
 explained method of predicting the basin of stability.  The classic example,
 that he used, proved that the Mandelbrot, being generated by inputting the
 equation to a circle, results in a cardioid basin of stability.

 This led me to investigate other plane curves being inputted and hopefully
 predict their particular basins of stability

 I have written a paper in WordPerfect, (involving equations and graphs), that
 I have converted to both HTML and PDF.  If any reader is interested  in this
 maths of fractals, I can provide a copy of my findings so far, and hopefully
 more development may be facilitated.


        I'm looking forward to participating in this forum, and
  hope to be able to contribute.
               Davrin                                                                                                       

Welcome to FF kind sir.
I think Ultra Fractal has this capability. They seem to deal well with equations in any case, and if there isn't a formula in their public collection to your liking you could always make one that fits better.

Sadly I'm not familiar with your area of research, but it's always good to get some variety around here to stir things up.

Welcome

Well, I did find several webpages that basically mentioned you here and there, but only one main page that had a full discussion you had written:
     http://www.wbabin.net/physics/halprin.htm

I skimmed over certain areas of it, specifically looking for references to fractals and chaos, and only found one sentence.  Hopefully further reading and searching will turn up more of what you have written about when it comes to fractals.

Here is the PDF you sent me:

http://www5.upload2.net/download/gbzDu3JsjC13F4G/lauw.pdf

If the above link doesn't work then use this one:
http://www.fractalforums.com/lauw.pdf