tile.jpg FRACTAL FIND
Explore Fractal and Quantum Variations

Lynn Wienck

CHAPTER 9
Mandelbrot Quantum Fractal Two Spin-1 Device Entanglement

Mandelbrot State Change Totals where zᵢ ≠ 0 + zⱼ ≠ 0
Section{-}{0}{+}Sum
x1,y1 6011993721 4521
x4,y2 0 0 60 60
x7,y327961442118 5058
x2,y4 22 1 21 44
x5,y5 0 0 0 0
x8,y6 33 1 9 43
x3,y71367 371201 2605
x6,y8 16 0 1 17
x9,y91711 49 194 1954
Sum6546431743514302
Quantum Fractal Entanglement
Both Mandelbrot zⱼ ≠ 0 and zᵢ ≠ 0 are necessary to provide a complete Mandelbrot map.
Mandlebrot zⱼ and zᵢ are entangled entities and the sum of both entities provides a complete map. The three parts of the map are described and shown below:

Mandelbrot (zⱼ where zⱼ ≠ 0 and zᵢ = 0)
zⱼ reflects points found only in the y-direction. There are 4964 zⱼ pixels.

Mandelbrot (zᵢ where zᵢ ≠ 0 and zⱼ = 0)
zᵢ reflects points found only in the x-direction. There are 4565 zᵢ pixels.

Mandelbrot (zⱼ ≠ 0 and zᵢ ≠ 0)
zⱼ ≠ 0 and zᵢ ≠ 0 reflect points in common in both the x-direction and the y-direction.
The points may be common to both zⱼ and zᵢ, but the state values are different.
There are 4773 zⱼ ≠ 0 and zᵢ ≠ 0 pixels.

To obtain the complete map, zⱼ ≠ 0, zᵢ ≠ 0 are summed yielding the map seen to the right:

Mandelbrot (zⱼ ≠ 0 + zᵢ ≠ 0)
There are 253009 pixels in the map, but only 14302 pixels where either zⱼ ≠ 0 or zᵢ ≠ 0 or both zⱼ ≠ 0, zᵢ ≠ 0.
There are 431 pixels where zⱼ ≠ 0 and zᵢ ≠ 0, but their sum (zⱼ ≠ 0 + zᵢ ≠ 0) = 0.
Just because you can't see it, doesn't mean it's not there.

c09.jpg c09.jpg
Mandelbrot (zⱼ) c09.jpg
Mandelbrot State Change Totals (zⱼ) where zⱼ ≠ 0 and zᵢ = 0
Section{-}{0}{+}Sum
y1 30 014231453
y2 0 0 54 54
y31945 0 451990
y4 0 0 11 11
y5 0 0 0 0
y6 8 0 2 10
y7 1 010471048
y8 0 0 1 1
y9 317 0 80 397
Sum2301 026634964
Mandelbrot State Change Totals (zⱼ) where zⱼ ≠ 0 and zᵢ ≠ 0
Section{-}{0}{+}Sum
y1 352 016882040
y2 0 0 2 2
y3 971 0 3371308
y4 8 0 15 23
y5 0 0 0 0
y6 17 0 6 23
y7 232 0 253 485
y8 3 0 0 3
y9 733 0 156 889
Sum2316 024574773
Mandelbrot (zᵢ) c09.jpg
Mandelbrot State Change Totals (zᵢ) where zᵢ ≠ 0 and zⱼ = 0
Section{-}{0}{+}Sum
x1 165 0 8631028
x2 9 0 1 10
x31049 0 231072
x4 0 0 4 4
x5 0 0 0 0
x6 13 0 0 13
x7 65 016951760
x8 6 0 4 10
x9 620 0 48 668
Sum1927 026384565
Mandelbrot State Change Totals (zᵢ) where zᵢ ≠ 0 and zⱼ ≠ 0
Section{-}{0}{+}Sum
x1 488 015522040
x2 16 0 7 23
x3 367 0 118 485
x4 0 0 2 2
x5 0 0 0 0
x6 3 0 0 3
x7 588 0 7201308
x8 19 0 4 23
x9 796 0 93 889
Sum2277 024964773