Funky Baby says it all!

Is this a 3D Mandelbrot? The Funky Baby is constructed using two Mandelbrot Babies: the original 2-D Mandelbrot and the sibling 3-D reflection - a MandelFash Baby. Wait until you see the complete 3-D MandelFash Baby; it is a beautiful thing.

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.

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 & 

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 it in a Horizontal 

or a Vertical chunk from the log at any point and 

 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 


Birth of a MandelFash Baby

This demonstration reveals the 3-D Sphere (Radius 2)

 that surrounds the 3-D MandelFash Egg Case in Red.  

The layering around the Mandelbrot is defined by 

LoopCount integer values; the LoopCounts increm-

ent from 1 to 1000  sequentially,  one-at-a-time.  

This video has inspired the creation of a manipula-

tive,  an object that can be used in a Math Class. 

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

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. 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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See Chapters in the "Why Mandelbrot?" video series at

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.

Instructional Math Tools, LLC.

West Melbourne, Florida 32904, USA