colouring job done by 
his attempts simply looked better than mine did...
Though, the formula is by me as always.
It's a reinterpretation of the Mset and a series of 3, where the first one actually is the standard Mandelbrot set.
you might know what the "i" in x+y*i means. It's one of two possible solutions for the squareroot of -1. (the other solution simply is -i ^^)
Additionally, it combines vectors with algebra.
This Complex Algebra can be generalized further in several ways.
One of those extensions can be viewed here.
The rule for i simply is:
i²=-1
there are two more ways to extend this. Here, I chose the one, fewer ppl probably would ever think about:
ε≠0 but ε²=0
(x+yε
² ->
x->x²
y->2xyε
as you see, this rule creates a nice simple fan pattern.
his attempts simply looked better than mine did...Though, the formula is by me as always.
It's a reinterpretation of the Mset and a series of 3, where the first one actually is the standard Mandelbrot set.
you might know what the "i" in x+y*i means. It's one of two possible solutions for the squareroot of -1. (the other solution simply is -i ^^)
Additionally, it combines vectors with algebra.
This Complex Algebra can be generalized further in several ways.
One of those extensions can be viewed here.
The rule for i simply is:
i²=-1
there are two more ways to extend this. Here, I chose the one, fewer ppl probably would ever think about:
ε≠0 but ε²=0
(x+yε
² ->x->x²
y->2xyε
as you see, this rule creates a nice simple fan pattern.
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:origin()/pre00/9fa0/th/pre/f/2012/134/6/a/amaterasu_by_kram1032-d4zpdbz.jpg)
:origin()/pre00/c63f/th/pre/f/2012/098/e/8/eye_cu_by_kram1032-d4vgka1.png)
:origin()/pre00/9933/th/pre/i/2011/070/2/7/sv3d_mset_xz_by_kram1032-d3bek76.png)
:origin()/pre00/4625/th/pre/i/2011/070/7/0/sv3d_mset_xy_by_kram1032-d3azw82.png)
:origin()/pre00/cb4b/th/pre/i/2010/233/5/4/royal_imagination_by_kram1032.png)
:origin()/pre00/8422/th/pre/i/2010/229/d/6/multicomplex_by_kram1032.png)
:origin()/pre00/723d/th/pre/f/2010/141/2/a/back_to_the_roots_by_kram1032.png)
:origin()/pre00/3acf/th/pre/i/2010/138/4/6/tribal_symbolism_by_kram1032.png)
:origin()/pre00/418e/th/pre/i/2014/044/4/4/crazy_big_stripe_swirl_by_andrea1981g-d769ecx.png)
:origin()/pre00/d863/th/pre/i/2010/155/b/8/carpe_diem_by_shadoweddancer.jpg)
:origin()/pre00/0458/th/pre/i/2009/351/f/b/polar_5_by_sparky650.jpg)
:origin()/pre00/81fc/th/pre/f/2018/275/e/a/501h2b_by_akurapare-dcodifj.jpg)
:origin()/pre00/f88c/th/pre/f/2018/275/7/1/501h2e_2_by_akurapare-dcodimv.jpg)
:origin()/pre00/c1e1/th/pre/f/2012/286/f/b/weird_floor_with_plates_by_andrea1981g-d5ho170.png)
:origin()/pre00/c78f/th/pre/f/2016/225/a/3/misty_forrest_of_another_time_and_dimension_by_pamonk-da6x0r5.png)
:origin()/pre00/e877/th/pre/f/2018/272/c/2/tile_trails_by_aureliuscat-dco2gra.jpg)
:origin()/pre00/b4ad/th/pre/i/2009/189/b/9/sunset_fans_by_kram1032.png)
What I do not yet understand is, why on earth quaternions, which obviously are an other way to extend complex numbers, have such weird multiplications.
I mean... ok... quaternions cease to have comunicative multiplication, so ij=-ji=k, or something...
but WHY do they have that? xD
Here is a little toy, to pass the time with: [link]
I know that toy already and use it a lot to simplify my formulae to make things go faster
Thanks anyway
hmmmmm... tea
Well, could you also answer me that?
Show me a way to proof the uncommuntativity of quaternions... It might help me...
It must follow somehow from the rules that i*j*k=i²=j²=k²=-1
also I'm kinda unsure, how the multiplication rules apply to division...
from i*j=k -> i=k/j and j=k/i ?
so j*i=-k -> j=-k/i and i=-k/i... that kinda doesn't make sense. Or, does it? that would mean, that i=-i which apparently isn't true either...
Wiki just derives the trivial k=i*j but doesn't directly show, why -k=j*i... It later refers to the cross product implying the reason but... oh well xD
Though, what I did now was this:
first step as Wiki said:
-1=ijk=i²=j²=k²
-i=ijki
-i=-jk
i=jk
-j=ijkj
-j=-ik
j=ik
-k=ijkk
-k=-ij
k=ij
and from those definitions, I went on, replacing each letter by the others:
i=jk, j=ik
i=ikk
i=-i FALSE
i=jk, k=ij
i=jij
i=-i FALSE
i=jk, j=ik, k=ji
i=ikji
i=-kj TRUE
same for the two others...
I wonder if that's the standard way to do the full derive...
but of course, it's always best to derive things yourself!
Oh well, so, at least I seem to have found the reason. Although it's very easy to do contradictions that way...