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

This is the most important video that I have ever made. It explains clearly why I can create a 3-D Mandelbrot, while Math Professionals say it is impossible. When a deep-thinking Professor listens to this video -- he/she will understand why it is NOT impossible to discuss Complex Numbers in a 3-D context.

Stay tuned for Part #2 -- it completes the argument.

CHAPTER 1 - The "Secret Sauce"

What is a function? How does "Recursion" work? How does Mandelbrot create his magic? Let us look closer and see if we have the eye to recognize the Secret Sauce

Chapter 2 - Complex Variables

Second in a six-part series of videos - answering the question: Why Mandelbrot?

Chapter 3 - The Algorithm

Third video in a series of 6 videos belonging to the series "Why Mandelbrot?" The video comes with a FREE Software Program, written in C++, which allows the novice to create their own Mandelbrot Baby. It also provides the capability to dive-deep into the beautiful fractals which surround the baby. DOWNLOAD THE PROGRAM -- DIRECTLY BELOW THIS VIDEO PRESENTATION.

Mandelbrot Generator in source C++ Code

This C++ Program generates Mandelbrot Babies and allows for deep dives into self-replicating fractals.  The instruction for installation and operation of this code is contained in the third in the series of 6 Videos, entitled "Why Mandelbrot?" -- Chapter 3 - The Algorithm. It is a free product -- offered with no guarantees and no acceptance of liability. One needs to participate in Chapter 3 video, prior to operating this software. This C++ code is intended for instructional purposes only and is considered a training aid - to teach you how to generate a Mandelbrot Baby and to zoom-in on areas of interest.

Chapter 4 - The Monsters

This series of videos is designed for the Mandelbrot enthusiast or for anyone wanting to learn more. Good to start with Chapter 1 - but this Chapter is stand-alone and I believe you will not only enjoy these brief 23 minutes, but you will be passing it on to your friends.

Chapter 5 - The Dimensions

Dimensions of Mandelbrot -- scaling, box counting, and 3D Siblings. The "Why Mandelbrot?" video series has arrived at the heart of Mandelbrot's  'happy place' -- discussing fractal coastlines and their roughness in the context of  Dimensions. Prepare yourself for non-integer dimensions; not 1-D or 2-D; but 1.456-D. Chapter 5 explores Scaling Factors, Box Counting, Linear Regression, 3D Complex Plane, Mandelbrot Siblings, and a special visit to the MandelFash Fractal Log. You will really enjoy this visit into other dimensions.

Note: MandelFash Fractal Log (c) 2019, Instructional Math Tools, LLC., FL USA

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 are just a triple of the Log, out for a family outing - dancing naked.

#Mandelbrot #MandelFash #FractaLog #Fashenpour

The MandelFash Babies are Dancing

When the 3-D MandelFash Siblings decide to go dancing, things get weird. Notice the touching, where the 'feathers' of each fin touch the feathers of the adjacent sibling. The most interesting area of this photo is the Baby living on the long proboscis -- notice how it is 3-D also with its own horizontal and vertical baby overlapping. That is when you know for sure that 3-D is in full-force; in this Complex Number Plane.

Fractal Log Infrastructure

With the top of the Log stripped-away, observe how the internal 'babies' are arranged in a strong cross-beam support structure. The REFLEXIVE nature of the internal MandelFash Babies provide an infinite number of horizontal and matching vertical babies.

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).

Spinning half of the MandelFash Fractal Log

It is this Log that creates both MandelFash Babies and the Mandelbrot Baby. Enjoy "Claudio the Worm" as you examine the MandelFash Fractal Log.

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Researching the 3-D Complex Plane

I have expanded the 2-D Complex Number Space into a 3-D Complex Number Space; 

using a proprietary computation technique (c) 2018-19.  I have identified a 3-D structure never before observed, 

which I call the MandelFash Fractal Log. Full explanation is in this Research Paper. But stand-by there is a technical text book 

being written/published as we speak - The Fractal Log - soon to be available on Amazon under brand name: iMathTools.



Contact Me

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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