Funky Baby says it all!

Is this a 3D Mandelbrot?

The Naked Mandelbrot - a view you have never seen.

Check out this great video -- fascinating aspects of the Mandelbrot Baby that no one has ever seen.

Revealing the egg-case which surrounds the baby, with waves of colors dictated by loop-counts 

(ignored by almost all 'experts'). You will see the Mandelbrot Baby with and without its clothes. 

Also see the "RINGS PROJECT-SPECS", an exciting downloadable PDF file -- below.

A Beautiful Equation - broken-down & made simple.

The simplicity of Mandelbrot's Recursive Equation is revealed for all to see.

You will actually understand this beautiful equation. There is also an easy

to follow explanation of binomial multiplication - where even the novice 

will want to see this equation work and to "Feel the Thunder".

Part #1 of the SECRET to 3D Complex Numbers.

This video provides insight into non-associative 3-D graphics, involved in Mandelbrot's Set of Complex Numbers. Further, it contrasts the 1850 frustrations of William Rowan Hamilton's attempts to establish an R3 Field with Benoit Mandelbrot's 1980 Recursive Equation; which eliminates the need for an R3 Field. See the video (below) to find-out what you can accomplish, thinking 'outside the box’.

See also  Part #2 which completes the argument, below this video.

Part #2 of the SECRET to 3D Complex Numbers.

In Part #1, the 3-D Secret is revealed, a secret that allows the creation of a 3-D Mandelbrot Baby.

 In Part #2 The MandelFash Fractal Log is analyzed and a variety of MandelFash Babies are generated by 

the "Baby Generator Tool" -- a  FREE tool which is made available via a web download and the

web address is given at the end of the presentation.

Triple-Squares Dancing

Who would have imagined... the MandelFash Fractal Log is REFLECTIVE!! You can slice a Horizontal/Vertical chunk from the log at any point and guess what? You get identical slices - one horizontal and the other vertical -- both identical. Here is a 'triple' of the Log, out for a family outing - dancing naked.

Birth of a MandelFash Baby

This demonstration reveals the 3-D Sphere (of Radius 2) that surrounds the 3-D MandelFash Egg Case in Red. The layering around the Mandelbrot is defined by Loop-Count integer values; the Loop-Counts increment from 1 to 1000 -- sequentially, one-at-a-time.  This video has inspired the creation of a manipulative,  an

object that can be used in a Mathematics classrooms. Stay tuned and see the "RINGS PROJECT-SPECS" 

 below this video, a Downloadable PDF File that contains manipulative design specs.

RINGS -- PROJECT SPECS (save it to your computer)

Here are the specifics of the Rings (Slices) of the Sphere of Radius 2; as the MandelFash mutates through the

stages of development in order to become a mature Mandelbrot Baby. These Specifications are  the design

 specs for a manipulative to be used in Mathematics classrooms to teach the concept of an actual 

SPHERE with Rings of 39 Color Transparencies supported by a 3-D printed support structure. 

 Would love to hear your opinions and your ideas. Go-ahead and download the

 "RINGS PROJECT-SPECS" to your computer.

Spaceship from Planet MandelFash

Looks strangely like some of our stealthiest weapon systems.

Claudio - the worm


The very long reach of the MandelFash Fractal Log


The Fractal Log is infinite -- reaching in from forever and creating MandelFash Babies.

I am Dave Fashenpour and I have a BS Degree in Math and an MS Degree in Comp Sci. I am a retired military officer and a retired Senior Software Engineer for the Boeing Company. I worked as a contractor for NASA at the Johnson Space Center in Houston, Texas for 20 years and helped with the planning and design of the International Space Station.       


 I have been working on a process to create a 3D Complex Plane -- a plane that modern math teachers say does not exist.  My efforts were successful and I have the evidence to prove it. Will the math community step-up and admit they missed this one?  I think not!  You know, pride and ego sometime get in the way; but if we relax and take a step back, we can observe a beautiful graphic image; an image  that reaches to +/- infinity.

 I have successfully discovered a previously invisible entity and have documented the MandelFash Fractal Log (c), Copyright 2018-19, by Instructional Math Tools, LLC., Melbourne, FL.  First, came the Naked Log and then the Sliced Log.


The Naked Log

The Naked MandelFash Fractal Log is a solid 3D object that surrounds the Mandelbrot Baby (discovered by Benoit Mandelbrot around 1980). The log is made-up of MandelFash Babies; an infinite amount of stacked babies with fractals all around, at least until they mutate into BLACK PIXELS at the end of the 'wings'. Somewhere, buried in the center of the MandelFash Fractal Log -- is the 2D Mandelbrot Baby. For over 40 years PEOPLE have tried to produce a 3D Mandelbrot, but all of them have FAILED. They hired artists and drew elaborate conceptual designs of what they THOUGHT was the 3D Mandelbrot. Programmers modified the equations that Mandelbrot had developed and said, yes this is it! But they were all wrong. WHY? They were all wrong because they did not incorporate the COMPLEX PLANE. The MandelFash Fractal Log consists of only COMPLEX VARIABLES.


The Sliced Log

The Sliced MandelFash Fractal Log reveals the make-up of the log. It consists of solid babies -- MandelFash Babies! Their fractals surround each slice, that is until the slicing approaches the end of the wings; there, they mutate into BLACK PIXELS (the same Mandelbrot Set Membership Pixels discovered in 1980). One can produce three (3) significant slices from the MandelFash Fractal Log. There is the famous DIAGONAL slice that cuts the log in half, there is the VERTICAL slice which slices this 45 degree-leaning log at 45 degrees, and finally there is the HORIZONTAL slice which again attacks this 45 degree-leaning log at a 45 degree cut (90 degrees from the vertical).

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Get a Research Project going as soon as possible. You do not want other researchers to confirm these 3D Complex Variables do exist! Don't you want your students to make their mark in the world of Fractal Mathematics? Wouldn't YOU like to be that student! (I will make sure you get all the data and tools necessary to succeed). Everything you need FREE with a Educational Users License -- just ask and tell me your plans.

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West Melbourne, Florida 32904, USA