Instructional Math Tools, LLC.
West Melbourne, Florida 32904, USA


FRACTAL LOG
Fractal Log Website


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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.



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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".



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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.



################## Part #1 #############

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.



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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.



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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 naked.



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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.



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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.

Click here for Rings-PDF File



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Looks strangely like some of our stealthiest weapon systems.



############ Cladio the Worm ##########

Enjoy!








CHAPTER 1 - The "Secret Sauce"



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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



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Complex Variables is the second video,
in a six-part series of videos;
answering the question:
Why Mandelbrot?





Chapter 3 - The Algorithm



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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.
Mandelbrot Generator in written in source C++ Code

This C++ Program generates Mandelbrot Babies and allows for
deep dives into fractals. Instruction for installation & operation
of this code is contained in Chapter 3 of this video series,
entitled "The Algorithm", this software is a free product; offered
with no guarantees and no acceptance of liability. One needs to
participate in the Chapter 3 video, prior to operating
this downloaded software package.

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.


Click Here to download the Mandelbrot Generator ZIP file





Chapter 4 - The Monsters



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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



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The "Why Mandelbrot?" video series has arrived at the heart
of Mandelbrot's favorite pasttime: which is discussing fractal
coastlines and their roughness in the context of Dimensions.

Prepare yourself for non-integer dimensions; not 1-D or 2-D;
but 1.4-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.






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Link to main website: Fractal Log dot Com:
Click Here to link to FractalLog.com





Link to main website: Fractal Log dot Com:
Click Here for FractalLog.com









Fractal Log (c) 2019, 2020, 2021; Instructional Math Tools, LLC., FL USA