Chapter 1 - the "Secret Sauce" is next.

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

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

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.

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.

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.

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

Mandelbrot lived in the Complex Plane and so do I.

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 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 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).

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

Boundary Values are essential in defining what is defined and undefined in the Mandelbrot world. In his 2-D world, the boundary is simply a circle of radius 2; in the MandelFash 3-D world, you would think a simple sphere of radius 2 would do the trick - but no. When you add-in the MandelFash Fractal Log (c) 2018-19 - everything changes.

Showing only half of the log, one can see the emergence of the infinite RODS, along with a message in Morse Code.

This video will tell you everything you need to know about the MandelFash Fractal Log.

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.

TECHNICAL RESEARCH PAPER (pdf)

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See our Fractal Tools at http://iMathTools.com

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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