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Author Topic: Tutorial #1 - Complex Multiplication is a rotation!  (Read 2893 times)
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cKleinhuis
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« on: September 20, 2012, 09:57:01 AM »

oh yeah, i finally managed to complete my little youtube channel with the fourth and last character that was planned,
it is the respectfull dr.wisenhimer serving as technical introducer, in his first show he is showing that complex multiplication
is a rotation, which is fundamental in understanding how it lead to the triplex algebra:

enjoy, like share AND comment  afro afro afro
<a href="http://www.youtube.com/v/9n5kve9HzRo&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/9n5kve9HzRo&rel=1&fs=1&hd=1</a>
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divide and conquer - iterate and rule - chaos is No random!
danwinter
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« Reply #1 on: September 20, 2012, 10:08:22 AM »

important to note the only (constructive wave interference) solution to
recusive addition (multiplication)
is golden ratio-
which predicts fractal (infinite / self organizing / centripetal) perfected compression

the mathematics
www.fractalfield.com/mathematicsoffusion

www.fractalfield.com/mathematicsoffusion
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Jules Ruis
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« Reply #2 on: September 20, 2012, 11:35:29 AM »

For the mathematical formula, see:

http://www.fractal.org/Formula-Mandelbulb.pdf

Jules.Ruis@fractal.org
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Jules J.C.M. Ruis
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LMarkoya
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« Reply #3 on: September 20, 2012, 05:07:22 PM »

It took me a while, but I am really starting to appreciate your genius Christian.....loved the idea of Dr Wisenhiemer.....a little help from some more visuals, and of course bringing back your calandar assistant would be most helpful

Great stuff....and good luck with that mechanism grin
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cKleinhuis
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« Reply #4 on: September 20, 2012, 05:32:24 PM »

It took me a while, but I am really starting to appreciate your genius Christian.....loved the idea of Dr Wisenhiemer.....a little help from some more visuals, and of course bringing back your calandar assistant would be most helpful

Great stuff....and good luck with that mechanism grin

you had doubts ?! and the girls are for the golden shirt guy exclusively wink plan was to attract buyers, but the experiment sex sells obviously did not work out, anyways, the golden shirt is inspired by disco stu from simpsons and will continue to have girls wink

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divide and conquer - iterate and rule - chaos is No random!
mejohnsn
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« Reply #5 on: September 20, 2012, 09:07:02 PM »

oh yeah, i finally managed to complete my little youtube channel with the fourth and last character that was planned,
it is the respectfull dr.wisenhimer serving as technical introducer, in his first show he is showing that complex multiplication
is a rotation, which is fundamental in understanding how it lead to the triplex algebra:

enjoy, like share AND comment  afro afro afro
<a href="http://www.youtube.com/v/9n5kve9HzRo&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/9n5kve9HzRo&rel=1&fs=1&hd=1</a>

I have yet to view the whole thing, but I can already make one important observation: one of the reasons the math books by Dr. Hermann Weyl and Roger Godement are such classics is because they avoid inexact statements like "complex multiplication
is a rotation". In what coordinate systems is this even true. Sure, complex multiplication by a number that has complex absolute value of 1 is a rotation, but not every complex number yields a rotation when multiplying.

In fact, I did get far enough to see that the good doctor was more precise in his statement: he did not say "complex multiplication is a rotation", he said, "this is a rotation and a stretching operation". The distinction is very important and easy to get right, so...
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M Benesi
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« Reply #6 on: September 20, 2012, 09:41:29 PM »

haahahahaa   smiley   awesome
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tyebillion
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« Reply #7 on: September 20, 2012, 11:59:05 PM »

Excellent tutorial, I liked your other videos too.  Now I know how the arithmetic is applied in 3 dimensions.  Thank you.  By the way, nice dancing!
« Last Edit: September 21, 2012, 12:04:05 AM by tyebillion » Logged
Rico
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« Reply #8 on: September 21, 2012, 12:10:46 AM »

"In fact, I did get far enough to see that the good doctor was more precise in his statement: he did not say "complex multiplication is a rotation", he said, "this is a rotation and a stretching operation". The distinction is very important and easy to get right, so..."
" complex multiplication by a number that has complex absolute value of 1 is a rotation, but not every complex number yields a rotation when multiplying "
...
"...one important observation..."
____

that should be said , thank you !
« Last Edit: September 21, 2012, 12:49:42 AM by Rico » Logged
thargor6
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« Reply #9 on: September 21, 2012, 01:23:00 AM »

missed two enormous mandelbulbs... err... I mean the awesome babe from the previous one ;-)

Arrrrr, just kidding, good job, Christian cheesy
« Last Edit: September 21, 2012, 01:24:59 AM by thargor6 » Logged
cKleinhuis
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« Reply #10 on: September 21, 2012, 03:14:05 AM »

you are all perfectly right, complex multiplication is a rotation exactly when magnitude is 1, BUT i was just showing that complex multiplication is by definition a rotation, hence "i" has magnitude 1 .... any tutorial section is going to be re-recorded until it is perfect, so thank you for criticism, and it will be taken care of in next issues

nice to see 1 posters in the forums, lols, great to have this as first post, feel welcome, and again thank you for constructive criticism!

omg, i am drunk right now....
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divide and conquer - iterate and rule - chaos is No random!
cKleinhuis
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« Reply #11 on: September 21, 2012, 03:15:56 AM »

missed two enormous mandelbulbs... err... I mean the awesome babe from the previous one ;-)

Arrrrr, just kidding, good job, Christian cheesy

dude: BEHAVE!

continue commenting AND criticising!
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divide and conquer - iterate and rule - chaos is No random!
cKleinhuis
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« Reply #12 on: September 25, 2012, 12:56:50 PM »

is a rotation". In what coordinate systems is this even true. Sure, complex multiplication by a number that has complex absolute value of 1 is a rotation, but not every complex number yields a rotation when multiplying.

just after some days of thought, the statement is correct, complex multiplication is a rotation, if the complex number has non 1 magnitude additional a stretching/scaling occurs, and as i showed in the video this holds even true for real numbers, a real number lying on the real positive plane is a rotation of degree 0 ... but nonetheless it is a rotation, and as i showed a multiplication with a negative real number is a rotation by 180 degrees ... and this viewing led to gauss multi interpretation and clearness of the complex number plane ... so, the statement is correct, and i dont wanted to interfere basic users with too much detail, although complex number systems are far over the head of the normal youtube videos, i stick to my plan to introduce methods and techniques that lead to the discovery of the mandelbulb, these videos serve multi purpose, the experienced may have fun viewing it, the questioning programmer might get a deeper understanding, and the normal guy might get interested in going deeper into the topic .... so, anyways than you for your response!
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divide and conquer - iterate and rule - chaos is No random!
M Benesi
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« Reply #13 on: October 03, 2012, 08:08:21 AM »

  Complex numbers are a quicker method of calculating rotations for integer n:

z^n = (a+ ib)^n

If you divide by the magnitude of the complex number before taking it to the power, it is a very quick way to calculate rotations. 

  For example, when you want to calculate cos(5*theta), with theta being the angle between y and z, you simply take the complex number
theta = angle between y and z

cos (5*theta) + i sin (5*theta) = [ (y+ iz)/ sqrt(y^2+z^2) ] ^ 5

  It happens to be quicker than calculating
theta= atan2 (y + iz)  AND    cos (5*theta)  AND  sin (5*theta)

in some (maybe most?) compilers. 

  And when you take this:    (x +  i sqrt(y^2+z^2) )^n

  You end up with the correct magnitude for the Mandelbulb because you did not divide out the magnitude before exponentiation. 

   The you only have to take your various parts and multiply them together:

new x:  real part of (x +  i sqrt(y^2+z^2) )^n

new y:  imaginary part of (x...yz)^n  * real part of  [ (y+ iz)/ sqrt(y^2+z^2) ] ^ n

new z: imaginary part of (x...z)^n *  imaginary part of [y..z]^n
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lxh
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« Reply #14 on: October 03, 2012, 09:04:32 AM »

Hmmm ... well, well. But if you divide the button before the machine is taking off the power, it is a very quick way to solve this problem. grin
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I've learned so much by my mistakes that I'm planing to do some more.
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