Title: Introduction of Davrin, recently joined Post by: davrin on October 15, 2006, 05:41:04 AM 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 Title: Re: Introduction of Davrin, recently joined Post by: Nahee_Enterprises on October 15, 2006, 06:33:17 AM Introduction: Davrin 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. Hey there, David Halprin !! Welcome to this particular Forum. :D Was wondering if you had a website or place that you upload information or images?? Title: Re: Introduction of Davrin, recently joined Post by: Zoom on October 15, 2006, 09:37:20 AM Welcome to FF kind sir.
Quote from: Davrin Because of the infinite variety of contrived fractals, that can be generated 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.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. 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. Title: Introduction of Davrin, recently joined Post by: Jules Ruis on October 15, 2006, 12:04:49 PM Dear Darvin,
Yes, I am very interested. Please send me a copy: Jules.Ruis@fractal.org Title: Re: Introduction of Davrin, recently joined Post by: alan2here on October 15, 2006, 01:38:53 PM Welcome
Title: Re: Introduction of Davrin, recently joined Post by: heneganj on October 15, 2006, 09:19:33 PM Welcome to the forums Davrin an excellent introduction. We would love to read any material you have to offer and can even provide the hosting of small documents. Look forward to your posts.
Title: Re: Introduction of Davrin, recently joined Post by: Nahee_Enterprises on October 16, 2006, 09:27:38 PM 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 (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. Title: Re: Introduction of Davrin, recently joined Post by: heneganj on October 16, 2006, 10:06:56 PM Welcome to the forums Davrin! An excellent introduction - we look forward to your contributions.
There isn't much Nahee_Enterprises doesn't know about fractal software or indeed any other fractal resource and I'm sure he'll be glad to point you in the right direction. Title: Re: Introduction of Davrin, recently joined Post by: heneganj on October 17, 2006, 01:02:36 PM Here is the PDF you sent me: http://www5.upload2.net/download/gbzDu3JsjC13F4G/lauw.pdf (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 (http://www.fractalforums.com/lauw.pdf) |