ordered

673e1050-3a4f-4a08-b4f6-2b24175e9258 61 15 12 decimal

&[DATE] &[TIME] - &[FILENAME]

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

Plot isocontour @ max [181.617] x y f x 2^y + 11 - (2^x y 2^+ 7 - (2^+ a - :

a 181.617 :

x y axes x y / - :

f axes 2 1 sys

data n Decimate collect every 'n' pairs range 1 data rows n range : k 1 : i range u k el data i 1 el : v k el data i 2 el : k k 1 + : 31 line for u v augment 31 line 31 line :

Gray C:\SmathFile\Himmelblau181617.bmp READBMP :

λ 85 :

iVBORw0KGgoAAAANSUhEUgAAAK8AAABsCAIAAACTjHU4AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAMhSURBVHhe7dZRgqsgDEDRt8m3/6V0qEmNVquAoBDu+VPbDjH3Y/69gA9qgKEGmLtr+H9GP4cnVKxB17umz37Tz/2gH0IdhWvQpU30VlH602v6DJcVq+HBxcif/qLPkKJADW2+fTnVlj7Gnks19Ph+5cy/6IdGlV+Dy3cnTTxFD/GczBpaOLo/0sSWPq4vp4Y7z4dAmhB6q47kGmofCMekCaG3yqGGjhVvIq0GUmhQwSaowYkiTSTUQArtu9gENTiUvSlq8ClvWdTgVsa+qMGz1JVRg3NJW6MG/+IXRw3+UQNWIndHDUOgBqzErI8aRkENWDndYEINAUF0jRqwcrxBahgLNcCUrCEgiK5RA1YONkgNw6EGmJI1BATRNWqAoQas/NpgTg0BQXSNGmCoAYYaYKgBpnANAUH0ixpgqAEru+ujhkFRAww1wFADDDXAUANWthukhnFRA0yxGkjBAWqAoQaYMjWQghtfq6SGoV2tgRQ8oQYYaoC5VAMpOJNfAym4tFwrNYwupwZS8IoaYJJrIAXHqAEmrQZS8C2hBlIYwbxlakBcDaQwCGqAOa+BFMZxUgMpDIUaYI5qGCqFMOyWPhvGPPK4NUx7359UHgV67d086XcNI7yCadFRY8Z/sl/LAYerIWPAdxF+X8tytIFqmHaaP93FrzdrOdSqBpfTilKjvYuY6HX/lrMMUUONud5F9P+6vkawGhzMtjWtrOJctX+/tq/Du61hWtNNE8nfCvS6E9sz+6zhqVmm19vNa9we1VsN0zoeHkTOEOh1k3aP56eG6f23NYIcKdDrZvw6ktbQ4ImTNH7+dxETvX7UwTG6r2F6yd0cXk4b6PW9Tv90xzWcztYyObzQWzVF/qEua4icrRcyzkzvFpL0m539F5k0W6dkxiV9EEe/86F343RTQ8ZsbsjskfQ7WVqvQSYM9Bo1WQ1BUy+dCO7XXA0SQaDXuNGqhuCpNUgBgV7jCd81BHeuRAoI9BqP2qkhqL0h+f1Ar9GG/RpEwYXJT830LhpzVIPQBSauUL/zoXfRtvMaZrrYOPoddCWhBrhHDfh4vf4A6gAO3KZtwXgAAAAASUVORK5CYII= Gray

Convert existing gray pixels to black N i 1 Gray rows range j 1 Gray cols range N i j el 0 Gray i j el λ ≤ 255 cases : for for N 21 line :

Gray Min Gray Max 21 mat 8525521 mat

<= Min valued gray 85

N N :

Extract black pixels r N rows : c N cols : k 1 : i 1 c range j 1 r range N j i el 1 ≤ X k el i : Y k el r j - : k k 1 + : 31 line No pixel if for for 41 line

XY X Y augment :

xy XY 456464 range 12 range el :

XY rows 464

Raw extraction to be cleaned

XY 173 75 173 25 - 2 2 mat 2 1 sys

xy 17335173341733317332173311733017329173281732792 mat

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 N

data StripX nest stripped in 'R' u data 1 col : v data 2 col : k 0 : i 1 data rows 1 - (range u i 1 + el u i el - 0 ≠ R k k 1 + : el u i el v i el 12 mat : 11 line StripX done if 11 line for Un-nest R v R 1 el : j 2 R rows range v v R j el stack : for v 91 line :

xy1 XY 1116 range 12 range el : S4 xy1 2 csort : S4 S4 23 S4 rows 12 submatrix : 31 sys

new XY 1 csort : S1 new StripX : S1 S1 2 S1 rows range 12 range el : 31 sys

profitable decimation
by pure coincidence.
Can't explain [9] ? XY XY 9 Decimate : S2 XY 15 XY rows range 12 range el : 21 sys

S3 1732712 mat :

S S4 5 Decimate S1 5 Decimate S2 S3 stack :

S rows 112

S2 S2 rows row 1733412 mat

isocontour S o 5 red plot :

10 - 14 20 14 2 2 mat isocontour 3 32 3 10 - 2 2 mat 3 1 sys

S 4103144185226268301134133882 mat

ordered S4 S2 S3 S1 S1 rows 1 range 12 range el stack :

Comments . . .

Intuitively and from other easier closed contour

this project should have as well 4 segments.

The project is on image pixel scale ...

NOT so easy to scale on the function isocurve

whereas no maths can do quick.

]]>

Isocurve ordered clockwise ...

ordered isocontour 2 1 sys 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 N ordered

ordered 410411412313314315316417418419420421522523624625626727728829830931103210331134113512361337133814391440154115421643174417451746184718481949195019512052205320542055205620572058205920602061206219631964196519661967186818691870177117721773177416751676167716781579158015811582158315841585158615871588158915901591169216931794179518961997209821992299231002410025101281023210336103401044410448104521035610360102641026810172101761008010084998899929896981009810498108981129811698120981249812898132981369714097144961489515293156911608716382166771677016863169561704917143172381733417327172231712017019169181681716716166151651516414163141621316113160121591215812157121561215511154111531115211151111501114911148111471114611145111441114311142111411114012139121381213712136121351213413133131321313113130131291412814127141261412515124151231512216121161201611917118171171711618115181141811319112191112011020109201082110721106221052210423103231022310124100249925982597269626952794279327922891289028892888288728862885278427832682268125802479247823772276217521742073207219711870186917681767166615651564146314621361136012591258115711561055105410539529518508498487477467456446436425415405394384374364354343333323313303292282272262252242232222212202192182172162152143133123114104958576673052 mat :

ordered axes 2 1 sys

x ordered 1 col : y ordered 2 col : 12 mat

Area Polygon wrt vertices coordinates A 12 / x i el y i 1 + el * x i 1 + el y i el * - (i 1 x rows 1 - sum * abs :

Perimeter  Polygon wrt vertices coordinates P x i 1 + el x i el - (2^y i 1 + el y i el - (2^+ sqrt i 1 x rows 1 - sum :

native ordered A P 21 mat 1317450321 mat

for continuous junction S1 S1 S1 rows 1 range 12 range el :

n 5 :

iso S4 n Decimate S2 2 Decimate S3 S1 n Decimate stack :

X ordered 1 col : Y ordered 2 col : 21 sys

Xo X Mean 1 round : Yo Y Mean 1 round : 21 sys

isodata iso o 4 red plot :

centered iso 1 col Xo - iso 2 col Yo - augment : isocenter centered o 4 red plot : 21 sys

isodata isocenter 1 1 sys S1 S4 S2 S3 1 1 el S3 1 2 el . 14 black 1 5 mat 4 1 sys

collect S1 n Decimate S4 n Decimate S2 2 Decimate S3 stack :

global collect o 5 red plot :

collect global

S1 S4 S2 S3 11 el S3 12 el . 14 black 15 mat 41 sys

Iso centered

iso 65.2 - 27.6 - 66.2 - 23.6 - 65.2 - 19.6 - 64.2 - 15.6 - 63.2 - 11.6 - 61.2 - 7.6 - 58.2 - 3.6 - 56.2 - 0.4 54.2 - 4.4 52.2 - 8.4 50.2 - 12.4 49.2 - 16.4 49.2 - 20.4 49.2 - 24.4 50.2 - 28.4 51.2 - 32.4 52.2 - 36.4 53.2 - 40.4 54.2 - 44.4 54.2 - 48.4 54.2 - 52.4 52.2 - 56.4 49.2 - 60.4 45.2 - 62.4 41.2 - 64.4 37.2 - 65.4 33.2 - 65.4 29.2 - 66.4 25.2 - 66.4 21.2 - 66.4 17.2 - 65.4 13.2 - 65.4 9.2 - 64.4 5.2 - 64.4 1.2 - 63.4 2.8 63.4 6.8 62.4 10.8 62.4 14.8 61.4 18.8 61.4 22.8 60.4 26.8 60.4 30.8 60.4 34.8 60.4 38.8 60.4 42.8 60.4 46.8 60.4 50.8 60.4 54.8 60.4 58.8 60.4 62.8 60.4 66.8 59.4 70.8 59.4 74.8 58.4 78.8 57.4 82.8 55.4 86.8 53.4 90.8 49.4 93.8 44.4 96.8 39.4 97.8 32.4 98.8 25.4 99.8 18.4 100.8 11.4 101.8 5.4 102.8 0.4 103.8 3.6 - 103.8 10.6 - 102.8 14.6 - 98.8 20.6 - 94.8 23.6 - 90.8 25.6 - 86.8 25.6 - 82.8 26.6 - 78.8 26.6 - 74.8 26.6 - 70.8 25.6 - 66.8 25.6 - 62.8 24.6 - 58.8 23.6 - 54.8 22.6 - 50.8 21.6 - 46.8 19.6 - 42.8 18.6 - 38.8 16.6 - 34.8 14.6 - 30.8 13.6 - 26.8 11.6 - 22.8 9.6 - 18.8 9.6 - 14.8 10.6 - 10.8 13.6 - 6.8 16.6 - 2.8 18.6 - 1.2 - 20.6 - 5.2 - 23.6 - 9.2 - 25.6 - 13.2 - 27.6 - 17.2 - 28.6 - 21.2 - 30.6 - 25.2 - 31.6 - 29.2 - 32.6 - 33.2 - 33.6 - 37.2 - 34.6 - 41.2 - 35.6 - 45.2 - 35.6 - 49.2 - 35.6 - 53.2 - 35.6 - 57.2 - 34.6 - 61.2 - 32.6 - 1102 mat :

x iso 1 col : y iso 2 col : 12 mat

Area Polygon wrt vertices coordinates A 12 / x i el y i 1 + el * x i 1 + el y i el * - (i 1 x rows 1 - sum * abs :

Perimeter  Polygon wrt vertices coordinates P x i 1 + el x i el - (2^y i 1 + el y i el - (2^+ sqrt i 1 x rows 1 - sum :

decimated iso centered A P 21 mat 1293148421 mat

native ordered 1317450321 mat

x collect 1 col : y collect 2 col : 12 mat

Area Polygon wrt vertices coordinates A 12 / x i el y i 1 + el * x i 1 + el y i el * - (i 1 x rows 1 - sum * abs :

Perimeter  Polygon wrt vertices coordinates P x i 1 + el x i el - (2^y i 1 + el y i el - (2^+ sqrt i 1 x rows 1 - sum :

S1 S4 S2 S3 4 1 sys

2 more points 
than iso-center A P 21 mat 1281748621 mat

iso rows collect rows 21 mat 11011221 mat

S1 S4 S2 S3 41 sys