The 3D Mandelbrot set. Part two.

With my previous post I thought that I am leaving behind a lot of readers into the woods. But the goal of this new website is making easy to digest updates.

Therefore just three pictures explaining a bit more about the 3D Mandelbrot set.
I wish the computer code writing folks a lot of luck; if you are the first that
has a view on the 3D Mandelbrot set you have won the race.

By the way; out there is something known as the Mandelbulb or so. It looks nice but believe it has nothing to do with the 3D Mandelbrot set. This Mandelbulb thing is not based upon a reliable way of multiplication in three dimensions, the results they found are nice looking but it is just not based on a rigid way of 3D multiplication…

Anyway, here are three pictures all sized 550 by 550 pixels that should shine a bit more light on the minds of those that write the code:

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On a video channel named Numberphile from Google they have a good explanation about how to color the pixels according to the Mandelbrot scheme. Here is the link:
The Mandelbrot Set – Numberphile

In all dimensions where complex numbers can be defined, you can do this…
Till updates, think well and live well.

Short stuff on the 3D Mandelbrot fractal.

About a year ago I decided to take about two years to make it to the 3D Mandelbrot set. So I tried to learn one of those modern programming languages like C++, I did build a new computer because on my old system C++ would not run. And so on and so on.

Decades ago I tried to learn a computer programing language known as Basic. When I found out how those kind of programming languages evaluted an integral, I almost had to vomit.
In those long lost years I already developed a fundamental dislike against programming.

Now I am 52 years of age and it is still the same; me writing computer code is not a happy thing to do. So I killed the project of being the first person on this planet to view the 3D Mandelbrot set using the 3D complex or circular multiplication…

I never made it beyond what is in C++ a ConsoleApllication; you get your output in an old fashioned DOS screen and no graphics at all. And how to embed this into a thing you can actually fly through, I have given up on that.

So I did not write much code, but the results had all you expected it should have: Strong sensitivity to initial conditions and so on and so on.

Well here is the kernel of the 3D Mandelbrot set for the circular multiplication.
Circular simply means we are using 3D circular numbers X = x + yj + zj^2 where j^3 = 1.

In this kernel we have to use so called ‘dummy variables’ because computers are so stupid you cannot tell them how to calculate the next round of variables This despite in the year 2016 most desktops have multiple cores, your programming language still uses the old von Neuman principles.

Here is the kernel with the dummy variables written as capital X, Y and Z while we only want to know how the x, y and z evolve over the iterations… :

int i = 1;
float x = 0f;
float y = 0f;
float z = 0f;
float X = 0f;
float Y = 0f;
float Z = 0f;

while ((i < 80)&(x*x + y*y + z*z < 1600))
{
i = i + 1;
X = x;
Y = y;
Z = z;
x = X * X + 2 * Y * Z + C0;
y = 2 * X * Y + Z * Z + C1;
z = Y * Y + 2 * X * Z + C2;
}

__________

0007=14Jan2016=Mandelbrot_in_3DOh oh my dear Mandelbrot baby, now I have thrown you into the river I will never be the first human to observe your intrinsic details. Let it be, let it be because for the rest of my life I can still hate that stupid computer code writing.

Till updates.

Some people will do everything wrong…

This is a very short update from a guy that likely goes under the name of Alen.
Now for years Alan has a very weird page hanging out there and he tries to describe the 3D complex numbers as they should be in his view…

Very very likely this is the approach Hmilton took for 12 to 15 years; it leads to all kinds of horrible difficulties, technical disasters and an end result useless to all people on the globe.

Now you must not jump to the conclusion that I hold this Alen person for some idiot. It is rumored that at any given time there are about 100 thousand professinal math workers out there and I do not mean high school teacher but people from the universities and stuff like that.

All these people cannot find higher dimensional complex number systems themselves either…
Ok, enough of the bla bla bla en prepare yourself to dive in the blurry and fuzzy mindset of how people thought 3D complex numbers must be (it is always with something squared that is minus one…):

N-DIMENSIONAL COMPLEX NUMBERS.
http://www.alenspage.net/ComplexNumbers.htm

Matrix representations and how to craft them.

Here it is still 01 jan 2016 so a happy new year.
In this update with five pictures with the standard size of 550 by 550 pixels we are going to look at how to craft matrix representations for higher dimensional complex numbers.

It is all rather basic stuff.

Here we go with post number 1 in the year 2016:

0006=01Jan2016=matrix_representation01

 

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Yeah yeah, every point of this graph represents a 3D complex number that if you craft the matrix representation of it, it is a unitary matrix.

So the next time you see a physics professional professor writing stuff like SU(3) you instantly know you are dealing with some form of idiot life…

Christmas post on magnetic monopoles.

This is a short update because this week I bought myself a second hand particle accelerator for just 6 €. It has a vacuum chamber and three electron cannons, the vacuum chamber is coated with phosphoric materials so that when particles from the cannons smash into it, a nice quantum related photon comes out.

This means: For 6 Euro I bought myself a small old color television.

It does not have much to do with higher dimensional complex numbers, but for myself speaking I think that all spin half particles are in fact magnetic monopoles.

Now since we live in the year 2015 we can also purchase rather cheap very strong magnets.
In the next photo you see a combination of those strong magnets with the three electron guns.

As you see on inspection: There is a circular part where the electrons do not reach the screen.
But in my view, if electrons were magnetic dipoles this would never happen.

Yet it happens… So think about it for a short time; what explains that weird circular ring where all electrons have gone void?

0006=where_are_the_electrons_gone

If those small electrons were magnetic dipoles, can you explain this result?

Have a nice Christmas & till updates.

From Hamilton to my first try.

It seems that the irish math guy sir Hamilton has sought three dimensional complex numbers for a staggering long period of 15 years. After 15 years he found the four dimensional quaternions, that is nice stuff but for differentiation and integration the quaternions are about the biggest disaster there is around.

Therefore, beside linear transformations, there is no functional analysis on the quaternions.

In this post I originally wanted to give you some link to some stuff that was labeled under the name ‘Alan’s pages’ but I cannot find them back. Alan did everything wrong just like Hamilton did:
Basically they start with the comlex and try this to extend to 3D space; that stuff is guaranteed to fail hard.
Anyway, my first try was a surface named the Riemann surface of the logarithm although at the time I found it I did not know what Riemann surfaces were. This update is five pictures long each 550 by 550 pixels. Have fun reading it.

0005=20Dec2015=Hamilton_and_first_try01

0005=20Dec2015=Hamilton_and_first_try02

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0005=20Dec2015=Hamilton_and_first_try04 0005=20Dec2015=Hamilton_and_first_try05In another development I wrote reason number 12 as why electrons have to be magnetic monopoles, later this week I will hang this into the other website on the page on magnetic stuff. It is about the plasma they use in nuclear fusion reactors, the plasma is not stable and the physics professors do not understand why this is.
Well these torus shaped fusion reactors constantly accelerate the plasma particles until they get relativety effects, the basic concept of torus shaped reactors is basically what is wrong with it…

Anyway, till updates.

Cauchy-Riemann equations for the complex plane and for 3D complex numbers.

 

In itself the name of ‘Cauchy-Riemann equations’ is a terrible way of naming these equations because it says nothing about why they are important.

It would be better to name the stuff involved like ‘Chain rule equations for partial derivatives’ because if that would be the case you would understand why these equations are worth your precious time anyway…

This update is 8 pictures of size 550 by 550 pixels or about 5 pages of A4 size if crafted in the A4 size format.
Now why are CR equations important?
Very simple: You can find the derivative of a function just like on the real number system or in the complex plane. That is why CR equations are the basic food for understanding higher dimensional complex number systems…

Enough of the bla bla, here are the 8 pictures:

 

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This stuff is basic stuff so it should be hanging out on this new website.

Till update my dear reader.

A short advertisement for 3D complex numbers.

To the date exactly 22 months ago on 09 Feb 2014 I posted that picture of an impression of a large black hole swallowing in matter and recycling a large fraction of that matter into energy.

I did do that because the structure of that plane and the two beams shooting out has a strong resemblense of how the non-invertible 3D complex numbers look:
That is a plane with a line perpendicular through it going through the 0 (of course 0 is the most non-invertible number in the world because it destroys all eigenvalues and not just a handfull of them).

For myself speaking I was under the impression that if the largests structures in the world look very much like 3D complex or circular numbers when it comes to non-invertability, one way or the other institutions like universities or academia would show some form of rudimentary interest.

After all every day all these university people always say they are in favor of progress.
Just as easy as we see zero point zero progress from all universities, just as easy we are once more years further down the timeline, just as easy we can jump to the conclusion university people do not want progress. They want to stick to the old and ancient ways because that is the way they behave day in day out, year in year out…

__________

Anyway, we have not talked on this website about how to figure out what numbers have an inverse and what numbers are invertable. So you have to believe on my word that in the next picture the given formulaes are just an approximation for those non-invertibles.
Do not worry about the 0.1 that is in there: It should be 0 but in that case the line perpendicular to the main plane would not be good visible.

After the bla bla, here is the short advertisement for 3D complex (and circular) numbers:

0003=09Dec2015=short-advertisement0003=09Dec2015=short-advertisement0003=09Dec2015=short-advertisement01

0003=09Dec2015=short-advertisement02So this is the conduct of the university people: If someone comes around with some good idea’s, why not stay silent year in year out decade in decade out?

But it has to be remarked that since the year 1990 the Dutch universities have been very good at burning tax payer money & that is the reason universities exist:
They are only there to burn tax payer money.

Till updates.

Eight pages on 6D numbers (containing 3D and 2D complex numbers).

The day before yesterday I finished an 8 page long update on six dimensional complex numbers from the viewpoint of inclusion and extension.

So basically I show that the complex plane and the 3D complex numbers are included in the 6D space while the other way around you can make a 6D space starting with the 2D and 3D complex spaces.
Link:
Inclusion and extension of complex spaces
http://kinkytshirts.nl/rootdirectory/just_some_math/3d_complex_stuff03.htm#06Dec2015

0002=02Dec2015=teaser_6D_complex_numbers

Well well, I still have a long learning curve to do on this new website because you can also make pictures shown at their real size…

Ok, now the previous website has gotten so much attention it would be time to post a bit more stuff in here. After all after just a few weeks and almost no content at all weirdly enough it already ranks relavtively high in the search engine stuff.

Another problem to be solved is that the comment section does not work and even the categories are disfunctional… Very likely this wordpress theme is developed by somebody that has no math insight at all. Why can I make categories while they do not work???
Beat’s me. Anyway, till updates.

Another proof the complex number i does not live in three dimensions…

When learning about higher dimensional complex numbers, one of the things you must first understand that the complex plane as known for centuries simply does not live in three dimensional space. If you look at it from a historical perspective people always tried to start with the two dimensional complex plane and tried to expand that into three dimensions.

It does not work that way; for example you can make 21-dimensional numbers by using 3-dimensional and 7-dimensional numbers. The dimension nicely breaks down via the prime number theorem (every natural number can be uniquely written as the factors of prime numbers).

Since 2 is not a divisor of 3, it is impossible to find the complex plane in a three dimensional world…

Now years ago I proved that for the complex multiplication the number i does not exist, yet now I started this new website why not give the same proof for the circular multiplication?

Click on the picture below to read that exiting proof… 😉
(On my browser I first have to click on the picture and after that enlarge it to get the readable stuff.)

0001=24Nov2015=i_lives_not_in_3D_proof

Picture size is 550 pixels wide by 1650 pixels high, I tried to write it in such a way that advanced high school folks could understand it.

Till updates.