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This little guy does polynomial equations!

Polynomial term structure models. Cheng, Tehranchi arxiv.org/abs/1504.03238 #q-fin

Polynomial term structure models. Cheng, Tehranchi arxiv.org/abs/1504.03238 #q-fin

polynomial Bodums...

 

Polynomial 9th class in telugu | how to find degree of polynomials | Types of polynomials based on degree

 

youtu.be/9tUGZjk6L6Y

  

Learn Class 10 Math by Er. Gyanesh Rai SIr

Graph of Quadratic Function by Gyanesh Rai Sir

knitting projects - an ipod cover which I made too large so now it's a camera case, a polynomial camera bag (video camera), and the robot toy (in progress) for Amelie. plus my pattern book with notes

SIMPLE = T / file does conform to FITS standard

BITPIX = -32 / number of bits per data pixel

NAXIS = 3 / number of data axes

NAXIS1 = 5374 / length of data axis 1

NAXIS2 = 3820 / length of data axis 2

NAXIS3 = 3 / length of data axis 3

EXTEND = T / FITS dataset may contain extensions

COMMENT FITS (Flexible Image Transport System) format is defined in 'Astronomy

COMMENT and Astrophysics', volume 376, page 359; bibcode: 2001A&A...376..359H

BZERO = 0. / Offset data range to that of unsigned short

BSCALE = 1. / Default scaling factor

PROGRAM = 'Siril 1.4.0-beta3' / Software that created this HDU

DATE = '2025-09-23T17:47:54' / UTC date that FITS file was created

DATE-OBS= '2025-09-19T02:13:29.072693' / YYYY-MM-DDThh🇲🇲ss observation start,

ROWORDER= 'TOP-DOWN' / Order of the rows in image array

EXPTIME = 1920.000032 / [s] Exposure time duration

OBSERVER= 'DaveMartin' / Observer name

FILTER = 'L_Enhance' / Active filter name

FOCALLEN= 958.112 / [mm] Focal length

CENTALT = 71.6030555555556 / [deg] Altitude of telescope

CENTAZ = 5.9475 / [deg] Azimuth of telescope

XBINNING= 1 / Camera binning mode

YBINNING= 1 / Camera binning mode

XPIXSZ = 3.76 / [um] Pixel X axis size

YPIXSZ = 3.76 / [um] Pixel Y axis size

INSTRUME= 'ZWO ASI2600MC Pro' / Instrument name

CCD-TEMP= -10. / [degC] CCD temperature

SET-TEMP= -10. / [degC] CCD temperature setpoint

GAIN = 100 / Sensor gain

OFFSET = 12 / Sensor gain offset

CVF = 0.2636 / [e-/ADU] Electrons per A/D unit

FOCPOS = 19517 / [step] Focuser position

FOCTEMP = 16.6800003051758 / [degC] Focuser temperature

OBJECT = 'SH2-131 (Elephants Trunk Nebula)' / Name of the object of interest

AIRMASS = 1.05356136208347 / Airmass at frame center (Gueymard 1993)

SITELAT = 39.3488888888889 / [deg] Observation site latitude

SITELONG= -78.8116666666667 / [deg] Observation site longitude

OBJCTRA = '21 38 58.944' / [H M S] Image center Right Ascension

OBJCTDEC= '+57 33 31.320' / [D M S] Image center Declination

RA = 324.74560100456 / [deg] Image center Right Ascension

DEC = 57.5587000403959 / [deg] Image center Declination

CTYPE1 = 'RA---TAN-SIP' / TAN (gnomic) projection + SIP distortions

CTYPE2 = 'DEC--TAN-SIP' / TAN (gnomic) projection + SIP distortions

CUNIT1 = 'deg ' / Unit of coordinates

CUNIT2 = 'deg ' / Unit of coordinates

EQUINOX = 2000. / Equatorial equinox

CRPIX1 = 2687.5 / Axis1 reference pixel

CRPIX2 = 1910.5 / Axis2 reference pixel

CRVAL1 = 324.74560100456 / [deg] Axis1 reference value

CRVAL2 = 57.5587000403959 / [deg] Axis2 reference value

LONPOLE = 180. / Native longitude of celestial pole

CDELT1 = -0.000224840737847169 / [deg] X pixel size

CDELT2 = 0.000224860686602583 / [deg] Y pixel size

PC1_1 = 0.345744287250735 / Linear transformation matrix (1, 1)

PC1_2 = 0.938328773849274 / Linear transformation matrix (1, 2)

PC2_1 = -0.938330570167512 / Linear transformation matrix (2, 1)

PC2_2 = 0.345739412114258 / Linear transformation matrix (2, 2)

A_ORDER = 3 / SIP polynomial degree, axis 1, pixel-to-sky

A_0_0 = 0.

A_1_0 = 0.

A_0_1 = 0.

A_2_0 = 5.62564045790263E-08

A_1_1 = -1.44264003374099E-07

A_0_2 = -2.62907849874921E-09

A_3_0 = -3.16722349744606E-10

A_2_1 = 1.10599484828326E-11

A_1_2 = -3.13649695720793E-10

A_0_3 = -2.23342416999306E-12

B_ORDER = 3 / SIP polynomial degree, axis 2, pixel-to-sky

B_0_0 = 0.

B_1_0 = 0.

B_0_1 = 0.

B_2_0 = -7.65455501576803E-08

B_1_1 = 7.05967389567685E-08

B_0_2 = -2.20775092582202E-07

B_3_0 = 2.07382079385262E-12

B_2_1 = -3.09765514137844E-10

B_1_2 = 7.27794524422538E-12

B_0_3 = -3.12142597386793E-10

AP_ORDER= 3 / SIP polynomial degree, axis 1, sky-to-pixel

AP_0_0 = 0.00102900889780615

AP_1_0 = -8.9930598753396E-06

AP_0_1 = 1.62058670307354E-07

AP_2_0 = -5.70851768899143E-08

AP_1_1 = 1.45881422780918E-07

AP_0_2 = 2.29168096201055E-09

AP_3_0 = 3.20298307622995E-10

AP_2_1 = -1.12667726861887E-11

AP_1_2 = 3.17553833757912E-10

AP_0_3 = 2.1819750011648E-12

BP_ORDER= 3 / SIP polynomial degree, axis 2, sky-to-pixel

BP_0_0 = -0.00118456837575966

BP_1_0 = -4.72855830088711E-08

BP_0_1 = -5.87266749085824E-06

BP_2_0 = 7.73338718101097E-08

BP_1_1 = -7.13332111664078E-08

BP_0_2 = 2.22521972331902E-07

BP_3_0 = -2.11218047480999E-12

BP_2_1 = 3.13215408322911E-10

BP_1_2 = -7.32837439405831E-12

BP_0_3 = 3.14814106367671E-10

PLTSOLVD= T / Siril internal solver

HISTORY Crop (x=138, y=47, w=5374, h=3820)

HISTORY Plate Solve

HISTORY Photometric CC (algorithm: SPCC)

HISTORY Trail Removal

HISTORY Trail Removal

HISTORY Trail Removal

HISTORY Background extraction (Correction: Subtraction)

HISTORY StatStretch: m=0.20 l=True n=True c=True b=0.00

HISTORY StatStretch: m=0.30 l=True n=True c=True b=0.00

HISTORY GHS LINEAR BP: 0.13

HISTORY GHS LINEAR BP: 0.03

HISTORY GHS pivot: 0.180, amount: 1.93, local: 0.00 [0.11 1.00]

HISTORY GHS INV pivot: 0.264, amount: 1.66, local: 0.00 [0.00 1.00]

HISTORY GHS pivot: 0.247, amount: 1.60, local: -2.23 [0.00 1.00]

HISTORY GraXpert AI denoise: strength 0.50

HISTORY GraXpert AI deconvolve: strength 0.50

HISTORY Saturation enhancement (amount=-0.37)

HISTORY SCNR (type=average neutral, amount=1.00, preserve=true)

HISTORY Curves Transformation with 3 points

HISTORY Curves Transformation with 3 points

PIERSIDE= 'WEST' /

CAMID = '1E1E560D0B020900' /

ADCBITS = 16 / Bit depth of camera sensor ADC in current mode

BIASADU = 121.16593933105469 / ADU for bias level (no photons) at current sett

EGAINSAV= 0.26355 / Electrons per ADU at saved bit depth

RELGAIN = 2.964 / Multiplicative gain relative to minumum

RDNOISE = 1.77 / Read noise in electrons

SUBEXP = 60.000001 /

COLORTYP= 'RGB' /

DATE-END= '2025-09-19T02:48:03.6317295' / System Clock:Est. Frame End

DATE-AVG= '2025-09-19T02:30:46.3522115' / System Clock:Est. Frame Mid Point

JD_UTC = 2460937.6047031507 / Julian Date at mid exposure

END

F(x) is a fourth order polynomial with integer coefficients and no common factor. The roots of F(x) are -2,-1,1,2. If p is prime number greater than 97, then the largest integer that divides F(p) for all values of p is: 

adjusted in GIMP, Brightness: -5, Contrast:45. Adjust Color Curves, curve type: 3rd degree polynomial. 09/26/2006

Polynomial Term Structure Models. Cheng, Tehranchi arxiv.org/abs/1404.6190 #q-fin

knitting projects - an ipod cover which I made too large so now it's a camera case, a polynomial camera bag (video camera), and the robot toy (in progress) for Amelie. plus my pattern book with notes

"The q^Volume Lozenge Tiling Model via Non–Hermitian Orthogonal Polynomials"

knitting projects - an ipod cover which I made too large so now it's a camera case, a polynomial camera bag (video camera), and the robot toy (in progress) for Amelie. plus my pattern book with notes

"Julia sets of rational maps converging to filled Julia sets of quadratic polynomials"

Gaby is fascinated by Bill's discourse on chaos theory and polynomial equations.

SIMPLE = T / file does conform to FITS standard

BITPIX = -32 / number of bits per data pixel

NAXIS = 3 / number of data axes

NAXIS1 = 3840 / length of data axis 1

NAXIS2 = 2160 / length of data axis 2

NAXIS3 = 3 / length of data axis 3

EXTEND = T / FITS dataset may contain extensions

COMMENT FITS (Flexible Image Transport System) format is defined in 'Astronomy

COMMENT and Astrophysics', volume 376, page 359; bibcode: 2001A&A...376..359H

BZERO = 0. / Offset data range to that of unsigned short

BSCALE = 1. / Default scaling factor

PROGRAM = 'Siril 1.4.0-beta4' / Software that created this HDU

FILENAME= 'M_42_Light_030.fits'

DATE = '2025-10-31T07:36:46' / UTC date that FITS file was created

DATE-OBS= '2025-09-23T03:42:13.745000' / YYYY-MM-DDThh🇲🇲ss observation start,

IMAGETYP= 'Light Frame' / Type of image

ROWORDER= 'BOTTOM-UP' / Order of the rows in image array

EXPTIME = 120. / [s] Exposure time duration

TELESCOP= 'ALTAIR 60ED 285@F\4.8' / Telescope used to acquire this image

FOCALLEN= 282.332 / [mm] Focal length

CENTALT = 36.58965 / [deg] Altitude of telescope

CENTAZ = 152.2026 / [deg] Azimuth of telescope

XBINNING= 1 / Camera binning mode

YBINNING= 1 / Camera binning mode

XPIXSZ = 2.90000009536743 / [um] Pixel X axis size

YPIXSZ = 2.90000009536743 / [um] Pixel Y axis size

INSTRUME= 'ZWO CCD ASI585MC Pro' / Instrument name

CCD-TEMP= 0. / [degC] CCD temperature

GAIN = 252 / Sensor gain

OFFSET = 10 / Sensor gain offset

FOCPOS = 4509 / [step] Focuser position

FOCTEMP = 12.88 / [degC] Focuser temperature

STACKCNT= 29 / Stack frames

LIVETIME= 3480. / [s] Exposure time after deadtime correction

EXPSTART= 2460941.61253818 / [JD] Exposure start time (standard Julian date)

EXPEND = 2460941.65571464 / [JD] Exposure end time (standard Julian date)

OBJECT = 'M 42 ' / Name of the object of interest

AIRMASS = 1.675606 / Airmass at frame center (Gueymard 1993)

SITELAT = 44.21667 / [deg] Observation site latitude

SITELONG= 3.733333 / [deg] Observation site longitude

OBJCTRA = '05 35 13.629' / [H M S] Image center Right Ascension

OBJCTDEC= '-05 23 30.733' / [D M S] Image center Declination

RA = 83.8067878837445 / [deg] Image center Right Ascension

DEC = -5.39187040713546 / [deg] Image center Declination

CTYPE1 = 'RA---TAN-SIP' / TAN (gnomic) projection + SIP distortions

CTYPE2 = 'DEC--TAN-SIP' / TAN (gnomic) projection + SIP distortions

CUNIT1 = 'deg ' / Unit of coordinates

CUNIT2 = 'deg ' / Unit of coordinates

EQUINOX = 2000. / Equatorial equinox

CRPIX1 = 1920.5 / Axis1 reference pixel

CRPIX2 = 1080.5 / Axis2 reference pixel

CRVAL1 = 83.8067878837445 / [deg] Axis1 reference value

CRVAL2 = -5.39187040713546 / [deg] Axis2 reference value

LONPOLE = 180. / Native longitude of celestial pole

CDELT1 = -0.000588455938499469 / [deg] X pixel size

CDELT2 = 0.000588583056461158 / [deg] Y pixel size

PC1_1 = 0.999971045287839 / Linear transformation matrix (1, 1)

PC1_2 = 0.00760976911259961 / Linear transformation matrix (1, 2)

PC2_1 = -0.00702752718973035 / Linear transformation matrix (2, 1)

PC2_2 = 0.999975306625917 / Linear transformation matrix (2, 2)

A_ORDER = 3 / SIP polynomial degree, axis 1, pixel-to-sky

A_0_0 = 0.

A_1_0 = 0.

A_0_1 = 0.

A_2_0 = 1.16911073765905E-07

A_1_1 = -1.11959906936081E-07

A_0_2 = 7.16908360650294E-09

A_3_0 = -6.76211241394976E-10

A_2_1 = -2.04692169387105E-12

A_1_2 = -6.69588888291091E-10

A_0_3 = -9.18538069637013E-12

B_ORDER = 3 / SIP polynomial degree, axis 2, pixel-to-sky

B_0_0 = 0.

B_1_0 = 0.

B_0_1 = 0.

B_2_0 = -2.89566112787058E-08

B_1_1 = 8.38622570492964E-08

B_0_2 = -1.43691782836682E-07

B_3_0 = 9.32418367917355E-12

B_2_1 = -6.49526526061618E-10

B_1_2 = -9.33393380767258E-12

B_0_3 = -6.82169296903145E-10

AP_ORDER= 3 / SIP polynomial degree, axis 1, sky-to-pixel

AP_0_0 = 0.00105211833932696

AP_1_0 = -9.2957364065116E-06

AP_0_1 = -1.1112805187518E-06

AP_2_0 = -1.18573994905131E-07

AP_1_1 = 1.13305179100407E-07

AP_0_2 = -7.9687737384666E-09

AP_3_0 = 6.83934757097103E-10

AP_2_1 = 2.35169800240733E-12

AP_1_2 = 6.79515280517906E-10

AP_0_3 = 1.05509269501993E-11

BP_ORDER= 3 / SIP polynomial degree, axis 2, sky-to-pixel

BP_0_0 = -0.000233826619013268

BP_1_0 = -1.77923941294731E-07

BP_0_1 = -6.20693370445569E-06

BP_2_0 = 2.92944919580771E-08

BP_1_1 = -8.46952465327864E-08

BP_0_2 = 1.44627980293916E-07

BP_3_0 = -9.4308911460658E-12

BP_2_1 = 6.56733254728743E-10

BP_1_2 = 1.0331309847295E-11

BP_0_3 = 6.8874448264194E-10

HISTORY GraXpert AI denoise: strength 0.76

FRAME = 'Light ' / Frame Type

APTDIA = 6.000E+01 / Telescope diameter (mm)

SCALE = 2.099193E+00 / arcsecs per pixel

PIERSIDE= 'WEST ' / West, looking East

RADECSYS= 'FK5 ' / RADECSYS

SECPIX1 = 2.0991930515E+00 / SECPIX1

SECPIX2 = 2.0991930515E+00 / SECPIX2

COMMENT Generated by INDI

WB_R = 5.500E+01 / White Balance - Red

WB_B = 7.500E+01 / White Balance - Blue

END

SIMPLE = T / file does conform to FITS standard

BITPIX = -32 / number of bits per data pixel

NAXIS = 3 / number of data axes

NAXIS1 = 1080 / length of data axis 1

NAXIS2 = 1920 / length of data axis 2

NAXIS3 = 3 / length of data axis 3

EXTEND = T / FITS dataset may contain extensions

COMMENT FITS (Flexible Image Transport System) format is defined in 'Astronomy

COMMENT and Astrophysics', volume 376, page 359; bibcode: 2001A&A...376..359H

BZERO = 0. / Offset data range to that of unsigned short

BSCALE = 1. / Default scaling factor

PROGRAM = 'Siril 1.4.0-beta2' / Software that created this HDU

DATE = '2025-06-06T02:26:58' / UTC date that FITS file was created

DATE-OBS= '2025-06-05T07:23:26.637448' / YYYY-MM-DDThh🇲🇲ss observation start,

IMAGETYP= 'Light ' / Type of image

EXPTIME = 20. / [s] Exposure time duration

TELESCOP= 'S50_123896fd' / Telescope used to acquire this image

FILTER = 'LP ' / Active filter name

APERTURE= 5. / Aperture of the instrument

FOCALLEN= 252.155 / [mm] Focal length

XBINNING= 1 / Camera binning mode

YBINNING= 1 / Camera binning mode

XPIXSZ = 2.9 / [um] Pixel X axis size

YPIXSZ = 2.9 / [um] Pixel Y axis size

INSTRUME= 'Seestar S50' / Instrument name

CCD-TEMP= 27.75 / [degC] CCD temperature

GAIN = 80 / Sensor gain

BAYERPAT= 'GRBG ' / Bayer color pattern

FOCPOS = 1757 / [step] Focuser position

STACKCNT= 180 / Stack frames

OBJECT = 'NGC 6334' / Name of the object of interest

SITELAT = 35.7785 / [deg] Observation site latitude

SITELONG= -86.8798 / [deg] Observation site longitude

OBJCTRA = '17 20 49.139' / [H M S] Image center Right Ascension

OBJCTDEC= '-36 05 58.010' / [D M S] Image center Declination

RA = 260.204747054455 / [deg] Image center Right Ascension

DEC = -36.0994472719422 / [deg] Image center Declination

CTYPE1 = 'RA---TAN-SIP' / TAN (gnomic) projection + SIP distortions

CTYPE2 = 'DEC--TAN-SIP' / TAN (gnomic) projection + SIP distortions

CUNIT1 = 'deg ' / Unit of coordinates

CUNIT2 = 'deg ' / Unit of coordinates

EQUINOX = 2000. / Equatorial equinox

CRPIX1 = 540.5 / Axis1 reference pixel

CRPIX2 = 960.5 / Axis2 reference pixel

CRVAL1 = 260.204747054455 / [deg] Axis1 reference value

CRVAL2 = -36.0994472719422 / [deg] Axis2 reference value

LONPOLE = 180. / Native longitude of celestial pole

CDELT1 = -0.000658033189222184 / [deg] X pixel size

CDELT2 = 0.000659868233640028 / [deg] Y pixel size

PC1_1 = 0.999988345894206 / Linear transformation matrix (1, 1)

PC1_2 = -0.0048278438014189 / Linear transformation matrix (1, 2)

PC2_1 = -0.00528635564140756 / Linear transformation matrix (2, 1)

PC2_2 = -0.999986027124396 / Linear transformation matrix (2, 2)

A_ORDER = 3 / SIP polynomial degree, axis 1, pixel-to-sky

A_0_0 = 0.

A_1_0 = 0.

A_0_1 = 0.

A_2_0 = -3.0185334739684E-07

A_1_1 = 3.79632122386144E-08

A_0_2 = -3.70915197339462E-08

A_3_0 = -1.20654093864682E-10

A_2_1 = -1.13978521220261E-10

A_1_2 = -1.29985902296438E-10

A_0_3 = 4.55527302970294E-11

B_ORDER = 3 / SIP polynomial degree, axis 2, pixel-to-sky

B_0_0 = 0.

B_1_0 = 0.

B_0_1 = 0.

B_2_0 = -1.35882943737208E-07

B_1_1 = -2.69079163994618E-07

B_0_2 = 3.07874215679794E-08

B_3_0 = -2.11573265015732E-10

B_2_1 = 4.23832778966718E-11

B_1_2 = -1.88424133637302E-11

B_0_3 = 4.62875065728235E-11

AP_ORDER= 3 / SIP polynomial degree, axis 1, sky-to-pixel

AP_0_0 = -8.84389145497515E-06

AP_1_0 = -4.57548943177954E-09

AP_0_1 = -4.26084654568386E-09

AP_2_0 = 3.01966407901219E-07

AP_1_1 = -3.79575953386013E-08

AP_0_2 = 3.71166944336262E-08

AP_3_0 = 1.20880624222883E-10

AP_2_1 = 1.13986740847137E-10

AP_1_2 = 1.300374021495E-10

AP_0_3 = -4.55482363125644E-11

BP_ORDER= 3 / SIP polynomial degree, axis 2, sky-to-pixel

BP_0_0 = -5.51609854703845E-06

BP_1_0 = -3.73644587659736E-09

BP_0_1 = -7.107501254211E-10

BP_2_0 = 1.3599780922515E-07

BP_1_1 = 2.69060331751485E-07

BP_0_2 = -3.07825180937418E-08

BP_3_0 = 2.11731109569427E-10

BP_2_1 = -4.22465822840259E-11

BP_1_2 = 1.88263359379871E-11

BP_0_3 = -4.62704850971526E-11

PLTSOLVD= T / Siril internal solver

HISTORY Plate Solve

HISTORY Photometric CC (algorithm: SPCC)

HISTORY Histogram Transf. (mid=0.046, lo=0.012, hi=1.000)

HISTORY Histogram Transf. (mid=0.123, lo=0.016, hi=1.000)

HISTORY Histogram Transf. (mid=0.270, lo=0.030, hi=1.000)

HISTORY Histogram Transf. (mid=0.360, lo=0.000, hi=1.000)

HISTORY Saturation enhancement (amount=0.10)

HISTORY NL-Bayes denoise (mod=1.000, CC enabled)

CREATOR = 'ZWO Seestar S50' / Capture software

PRODUCER= 'ZWO ' / Powered by ZWO

XORGSUBF= 0 / Subframe X position in binned pixels

YORGSUBF= 0 / Subframe Y position in binned pixels

EQMODE = 1 / Equatorial mode

CCDXBIN = 1 / Camera X Bin

CCDYBIN = 1 / Camera Y Bin

TOTALEXP= 3600. / Total Exposure Time in seconds

IMAGEW = 1080 / Image width, in pixels.

IMAGEH = 1920 / Image height, in pixels.

BG-EXTR = 'GraXpert'

CBG-1 = 0.013110694

CBG-2 = 0.013110694

CBG-3 = 0.013110694

INTP-OPT= 'AI '

HIERARCH SMOOTHING = 0.5

HIERARCH CORR-TYPE = 'Subtraction'

HIERARCH BGE-AI-VER = '1.0.1 '

END

 

SIMPLE = T / file does conform to FITS standard

BITPIX = -32 / number of bits per data pixel

NAXIS = 3 / number of data axes

NAXIS1 = 913 / length of data axis 1

NAXIS2 = 1841 / length of data axis 2

NAXIS3 = 3 / length of data axis 3

EXTEND = T / FITS dataset may contain extensions

COMMENT FITS (Flexible Image Transport System) format is defined in 'Astronomy

COMMENT and Astrophysics', volume 376, page 359; bibcode: 2001A&A...376..359H

BZERO = 0. / Offset data range to that of unsigned short

BSCALE = 1. / Default scaling factor

PROGRAM = 'Siril 1.4.0-beta2' / Software that created this HDU

FILENAME= 'Light_M 102_20.0s_IRCUT_20250629-005018.fit'

DATE = '2025-06-30T01:26:58' / UTC date that FITS file was created

DATE-OBS= '2025-06-29T05:49:53.952312' / YYYY-MM-DDThh🇲🇲ss observation start,

IMAGETYP= 'Light ' / Type of image

ROWORDER= 'BOTTOM-UP' / Order of the rows in image array

EXPTIME = 20. / [s] Exposure time duration

TELESCOP= 'S50_f1c10930' / Telescope used to acquire this image

FILTER = 'IRCUT_Starless' / Active filter name

APERTURE= 5. / Aperture of the instrument

FOCALLEN= 252.022 / [mm] Focal length

XBINNING= 1 / Camera binning mode

YBINNING= 1 / Camera binning mode

XPIXSZ = 2.90000009536743 / [um] Pixel X axis size

YPIXSZ = 2.90000009536743 / [um] Pixel Y axis size

INSTRUME= 'Seestar S50' / Instrument name

CCD-TEMP= 30.5 / [degC] CCD temperature

GAIN = 80 / Sensor gain

FOCPOS = 1611 / [step] Focuser position

STACKCNT= 85 / Stack frames

LIVETIME= 1700. / [s] Exposure time after deadtime correction

EXPSTART= 2460855.72417604 / [JD] Exposure start time (standard Julian date)

EXPEND = 2460855.75372505 / [JD] Exposure end time (standard Julian date)

OBJECT = 'M 102 ' / Name of the object of interest

SITELAT = 41.7559 / [deg] Observation site latitude

SITELONG= -88.1817 / [deg] Observation site longitude

OBJCTRA = '16 41 51.501' / [H M S] Image center Right Ascension

OBJCTDEC= '+36 27 36.355' / [D M S] Image center Declination

RA = 250.464587276909 / [deg] Image center Right Ascension

DEC = 36.4600986199018 / [deg] Image center Declination

CTYPE1 = 'RA---TAN-SIP' / TAN (gnomic) projection + SIP distortions

CTYPE2 = 'DEC--TAN-SIP' / TAN (gnomic) projection + SIP distortions

CUNIT1 = 'deg ' / Unit of coordinates

CUNIT2 = 'deg ' / Unit of coordinates

EQUINOX = 2000. / Equatorial equinox

CRPIX1 = 433.5 / Axis1 reference pixel

CRPIX2 = 902.5 / Axis2 reference pixel

CRVAL1 = 250.483565510496 / [deg] Axis1 reference value

CRVAL2 = 36.4476174834571 / [deg] Axis2 reference value

LONPOLE = 180. / Native longitude of celestial pole

CDELT1 = -0.00065927520653439 / [deg] X pixel size

CDELT2 = 0.000659322642324384 / [deg] Y pixel size

PC1_1 = 0.999827509892731 / Linear transformation matrix (1, 1)

PC1_2 = -0.0185728420469678 / Linear transformation matrix (1, 2)

PC2_1 = 0.0185463172349008 / Linear transformation matrix (2, 1)

PC2_2 = 0.999828002266901 / Linear transformation matrix (2, 2)

A_ORDER = 3 / SIP polynomial degree, axis 1, pixel-to-sky

A_0_0 = 0.

A_1_0 = 0.

A_0_1 = 0.

A_2_0 = -3.44412650883486E-07

A_1_1 = 2.75907537965136E-08

A_0_2 = -4.08823342747532E-08

A_3_0 = -1.62054654272883E-10

A_2_1 = -1.09740045666968E-10

A_1_2 = -1.01392495165323E-10

A_0_3 = -3.0846120082332E-11

B_ORDER = 3 / SIP polynomial degree, axis 2, pixel-to-sky

B_0_0 = 0.

B_1_0 = 0.

B_0_1 = 0.

B_2_0 = -1.69783919101058E-08

B_1_1 = -2.61216316640459E-07

B_0_2 = -3.95723621564852E-08

B_3_0 = 1.63142622636423E-10

B_2_1 = 9.12997712281894E-11

B_1_2 = 1.41523422073829E-12

B_0_3 = 3.15180475126433E-11

AP_ORDER= 3 / SIP polynomial degree, axis 1, sky-to-pixel

AP_0_0 = -8.02161477874444E-06

AP_1_0 = -4.51503967546785E-09

AP_0_1 = -1.98998890662477E-09

AP_2_0 = 3.44545405883865E-07

AP_1_1 = -2.75328548463217E-08

AP_0_2 = 4.09006021935603E-08

AP_3_0 = 1.62326466805082E-10

AP_2_1 = 1.09735943554347E-10

AP_1_2 = 1.01459125940644E-10

AP_0_3 = 3.08512125492036E-11

BP_ORDER= 3 / SIP polynomial degree, axis 2, sky-to-pixel

BP_0_0 = 1.18038190003934E-06

BP_1_0 = 4.52180702145043E-09

BP_0_1 = 5.34869482038403E-10

BP_2_0 = 1.69192630309624E-08

BP_1_1 = 2.61195426413813E-07

BP_0_2 = 3.95757184049428E-08

BP_3_0 = -1.63164025899456E-10

BP_2_1 = -9.11720827353905E-11

BP_1_2 = -1.40317676871498E-12

BP_0_3 = -3.15020128242472E-11

CREATOR = 'ZWO Seestar S50' / Capture software

PRODUCER= 'ZWO ' / Powered by ZWO

XORGSUBF= 0 / Subframe X position in binned pixels

YORGSUBF= 0 / Subframe Y position in binned pixels

EQMODE = 1 / Equatorial mode

CCDXBIN = 1 / Camera X Bin

CCDYBIN = 1 / Camera Y Bin

TOTALEXP= 20. / Total Exposure Time in seconds

BG-EXTR = 'GraXpert'

CBG-1 = 0.0038092358

CBG-2 = 0.0038092358

CBG-3 = 0.0038092358

INTP-OPT= 'RBF '

HIERARCH SMOOTHING = 0.5

HIERARCH CORR-TYPE = 'Subtraction'

HIERARCH SAMPLE-SIZE = 15

HIERARCH RBF-KERNEL = 'thin_plate'

HIERARCH SPLINE-ORDER = 3

BG-PTS = '[[21, 9, 1], [123, 39, 1], [195, 9, 1], [252, 24, 1], [309, 9, 1], &'

CONTINUE '[381, 39, 1], [453, 39, 1], [555, 39, 1], [597, 39, 1], [669, 39, &'

CONTINUE '1], [771, 9, 1], [843, 9, 1], [885, 39, 1], [957, 9, 1], [1029, &'

CONTINUE '39, 1], [51, 81, 1], [93, 111, 1], [165, 111, 1], [237, 111, 1], &'

CONTINUE '[339, 81, 1], [381, 81, 1], [453, 111, 1], [525, 81, 1], [597, &'

CONTINUE '111, 1], [669, 111, 1], [771, 111, 1], [843, 111, 1], [885, 81, &'

CONTINUE '1], [957, 81, 1], [1044, 96, 1], [51, 183, 1], [108, 168, 1], &'

CONTINUE '[165, 153, 1], [267, 153, 1], [324, 168, 1], [396, 168, 1], [453, &'

CONTINUE '153, 1], [525, 153, 1], [612, 168, 1], [699, 153, 1], [771, 153, &'

CONTINUE '1], [813, 153, 1], [915, 153, 1], [957, 153, 1], [1029, 153, 1], &'

CONTINUE '[36, 240, 1], [123, 255, 1], [195, 255, 1], [188.72964169381112, &'

CONTINUE '236.6123778501629, 1.0], [324.23452768729635, 137.58957654723127, &'

CONTINUE '1.0], [411, 225, 1], [453, 225, 1], [525, 225, 1], [597, 225, 1], &'

CONTINUE '[684, 240, 1], [741, 225, 1], [843, 255, 1], [885, 255, 1], [987, &'

CONTINUE '225, 1], [1059, 225, 1], [51, 327, 1], [93, 327, 1], [165, 327, &'

CONTINUE '1], [237, 327, 1], [99.08794788273622, 440.91205211726384, 1.0], &'

CONTINUE '[156.41693811074924, 466.9706840390879, 1.0], [571.2703583061889, &'

CONTINUE '328.3387622149837, 1.0], [525, 297, 1], [627, 297, 1], [684, 312, &'

CONTINUE '1], [771, 297, 1], [813, 327, 1], [885, 297, 1], [957, 297, 1], &'

CONTINUE '[1029, 327, 1], [51, 369, 1], [93, 369, 1], [165, 399, 1], [237, &'

CONTINUE '399, 1], [309, 399, 1], [214.78827361563526, 478.43648208469057, &'

CONTINUE '1.0], [662.9967426710098, 413.81107491856676, 1.0], [555, 369, 1], &'

CONTINUE '[597, 369, 1], [684, 384, 1], [741, 399, 1], [813, 369, 1], [885, &'

CONTINUE '369, 1], [957, 369, 1], [1059, 369, 1], [51, 471, 1], [108, 456, &'

CONTINUE '1], [165, 471, 1], [237, 471, 1], [309, 471, 1], &'

CONTINUE '[695.3094462540716, 325.21172638436485, 1.0], [658.827361563518, &'

CONTINUE '471.1400651465798, 1.0], [741.1726384364822, 526.3843648208469, &'

CONTINUE '1.0], [627, 441, 1], [699, 471, 1], [771, 441, 1], [843, 441, 1], &'

CONTINUE '[885, 471, 1], [987, 441, 1], [1044, 456, 1], [21, 513, 1], [123, &'

CONTINUE '513, 1], [165, 513, 1], [237, 543, 1], [309, 543, 1], &'

CONTINUE '[730.7491856677525, 365.86319218241044, 1.0], [81.36807817589579, &'

CONTINUE '543.0618892508144, 1.0], [154.33224755700326, 398.1758957654723, &'

CONTINUE '1.0], [709.9022801302933, 558.6970684039088, 1.0], [669, 513, 1], &'

CONTINUE '[741, 513, 1], [813, 513, 1], [915, 513, 1], [987, 513, 1], [1029, &'

CONTINUE '543, 1], [51, 615, 1], [108, 600, 1], [195, 615, 1], [237, 585, &'

CONTINUE '1], [309, 585, 1], [350.2931596091205, 627.4918566775244, 1.0], &'

CONTINUE '[669.2508143322475, 619.1530944625407, 1.0], [758.8925081433226, &'

CONTINUE '790.0977198697068, 1.0], [699, 615, 1], [771, 585, 1], [843, 585, &'

CONTINUE '1], [885, 585, 1], [957, 585, 1], [1059, 585, 1], [21, 657, 1], &'

CONTINUE '[93, 657, 1], [165, 657, 1], [237, 657, 1], [339, 657, 1], [411, &'

CONTINUE '687, 1], [836.0260586319218, 792.1824104234528, 1.0], [627, 657, &'

CONTINUE '1], [669, 657, 1], [771, 657, 1], [843, 657, 1], [915, 657, 1], &'

CONTINUE '[957, 657, 1], [1059, 657, 1], [36, 744, 1], [93, 729, 1], [195, &'

CONTINUE '759, 1], [237, 729, 1], [339, 729, 1], [396, 744, 1], [453, 759, &'

CONTINUE '1], [853.7459283387623, 1012.1172638436483, 1.0], [627, 729, 1], &'

CONTINUE '[669, 759, 1], [741, 729, 1], [843, 729, 1], [915, 729, 1], [987, &'

CONTINUE '729, 1], [1059, 729, 1], [51, 831, 1], [108, 816, 1], [165, 801, &'

CONTINUE '1], [237, 801, 1], [339, 831, 1], [381, 801, 1], [453, 801, 1], &'

CONTINUE '[305.47231270358316, 914.1368078175897, 1.0], [627, 801, 1], [669, &'

CONTINUE '801, 1], [741, 801, 1], [813, 831, 1], [885, 831, 1], [957, 831, &'

CONTINUE '1], [1029, 801, 1], [51, 903, 1], [93, 873, 1], [195, 873, 1], &'

CONTINUE '[237, 903, 1], [339, 873, 1], [381, 873, 1], [240.8469055374594, &'

CONTINUE '961.042345276873, 1.0], [525, 903, 1], [684, 888, 1], [771, 873, &'

CONTINUE '1], [843, 873, 1], [885, 873, 1], [957, 873, 1], [1044, 888, 1], &'

CONTINUE '[21, 945, 1], [123, 945, 1], [165, 945, 1], [237, 945, 1], [339, &'

CONTINUE '945, 1], [381, 975, 1], [419.0879478827361, 953.7459283387622, &'

CONTINUE '1.0], [140.7817589576548, 988.14332247557, 1.0], [771, 945, 1], &'

CONTINUE '[843, 945, 1], [915, 975, 1], [987, 945, 1], [1029, 945, 1], [21, &'

CONTINUE '1047, 1], [123, 1047, 1], [165, 1017, 1], [267, 1017, 1], [309, &'

CONTINUE '1017, 1], [381, 1047, 1], [483, 1017, 1], [525, 1047, 1], [669, &'

CONTINUE '1047, 1], [771, 1047, 1], [813, 1047, 1], [915, 1047, 1], [987, &'

CONTINUE '1017, 1], [1029, 1017, 1], [36, 1104, 1], [108, 1104, 1], [195, &'

CONTINUE '1119, 1], [267, 1089, 1], [324, 1104, 1], [381, 1089, 1], [483, &'

CONTINUE '1089, 1], [525, 1089, 1], [627, 1119, 1], [699, 1089, 1], [741, &'

CONTINUE '1119, 1], [843, 1089, 1], [915, 1089, 1], [957, 1089, 1], [1044, &'

CONTINUE '1104, 1], [21, 1161, 1], [123, 1161, 1], [195, 1161, 1], [237, &'

CONTINUE '1161, 1], [339, 1161, 1], [381, 1161, 1], [453, 1191, 1], [525, &'

CONTINUE '1161, 1], [627, 1191, 1], [699, 1191, 1], [741, 1161, 1], [813, &'

CONTINUE '1191, 1], [900, 1176, 1], [972, 1176, 1], [1059, 1161, 1], [21, &'

CONTINUE '1263, 1], [123, 1233, 1], [165, 1233, 1], [252, 1248, 1], [309, &'

CONTINUE '1233, 1], [381, 1263, 1], [453, 1233, 1], [699, 1233, 1], [771, &'

CONTINUE '1233, 1], [813, 1233, 1], [885, 1263, 1], [987, 1233, 1], [1059, &'

CONTINUE '1263, 1], [21, 1305, 1], [108, 1320, 1], [195, 1305, 1], [237, &'

CONTINUE '1305, 1], [324, 1320, 1], [411, 1305, 1], [453, 1305, 1], [525, &'

CONTINUE '1335, 1], [597, 1335, 1], [699, 1305, 1], [756, 1320, 1], [828, &'

CONTINUE '1320, 1], [900, 1320, 1], [987, 1335, 1], [1029, 1335, 1], [36, &'

CONTINUE '1392, 1], [123, 1377, 1], [195, 1377, 1], [237, 1407, 1], [339, &'

CONTINUE '1377, 1], [381, 1377, 1], [468, 1392, 1], [540, 1392, 1], [597, &'

CONTINUE '1377, 1], [699, 1377, 1], [741, 1407, 1], [843, 1377, 1], [900, &'

CONTINUE '1392, 1], [987, 1407, 1], [1029, 1377, 1], [51, 1479, 1], [123, &'

CONTINUE '1449, 1], [195, 1449, 1], [237, 1449, 1], [324, 1464, 1], [381, &'

CONTINUE '1449, 1], [453, 1449, 1], [525, 1449, 1], [597, 1449, 1], [699, &'

CONTINUE '1479, 1], [771, 1479, 1], [843, 1449, 1], [885, 1479, 1], [987, &'

CONTINUE '1479, 1], [1059, 1449, 1], [36, 1536, 1], [93, 1521, 1], [195, &'

CONTINUE '1521, 1], [237, 1521, 1], [339, 1551, 1], [381, 1521, 1], [453, &'

CONTINUE '1521, 1], [525, 1551, 1], [612, 1536, 1], [699, 1551, 1], [741, &'

CONTINUE '1521, 1], [813, 1551, 1], [885, 1521, 1], [957, 1521, 1], [1029, &'

CONTINUE '1521, 1], [21, 1623, 1], [93, 1593, 1], [165, 1623, 1], [237, &'

CONTINUE '1623, 1], [324, 1608, 1], [381, 1593, 1], [453, 1593, 1], [525, &'

CONTINUE '1623, 1], [597, 1623, 1], [699, 1593, 1], [771, 1623, 1], [813, &'

CONTINUE '1593, 1], [915, 1623, 1], [957, 1623, 1], [1029, 1593, 1], [51, &'

CONTINUE '1665, 1], [108, 1680, 1], [180, 1680, 1], [237, 1665, 1], [309, &'

CONTINUE '1665, 1], [381, 1695, 1], [483, 1695, 1], [525, 1695, 1], [597, &'

CONTINUE '1695, 1], [684, 1680, 1], [771, 1665, 1], [843, 1695, 1], [915, &'

CONTINUE '1695, 1], [957, 1695, 1], [1029, 1665, 1], [21, 1767, 1], [108, &'

CONTINUE '1752, 1], [165, 1737, 1], [237, 1767, 1], [309, 1767, 1], [411, &'

CONTINUE '1737, 1], [483, 1737, 1], [525, 1737, 1], [627, 1737, 1], [699, &'

CONTINUE '1737, 1], [741, 1767, 1], [828, 1752, 1], [915, 1737, 1], [957, &'

CONTINUE '1767, 1], [1029, 1767, 1], [51, 1839, 1], [93, 1809, 1], [165, &'

CONTINUE '1809, 1], [237, 1839, 1], [309, 1809, 1], [411, 1809, 1], [483, &'

CONTINUE '1809, 1], [525, 1809, 1], [597, 1839, 1], [699, 1809, 1], [741, &'

CONTINUE '1809, 1], [843, 1839, 1], [885, 1809, 1], [987, 1809, 1], [1059, &'

CONTINUE '1839, 1], [51, 1911, 1], [93, 1881, 1], [180, 1896, 1], [252, &'

CONTINUE '1896, 1], [339, 1881, 1], [411, 1911, 1], [483, 1911, 1], [555, &'

CONTINUE '1911, 1], [597, 1881, 1], [669, 1911, 1], [741, 1881, 1], [843, &'

CONTINUE '1911, 1], [915, 1911, 1], [957, 1911, 1], [1059, 1911, 1]]'

END

 

SIMPLE = T / file does conform to FITS standard

BITPIX = 16 / number of bits per data pixel

NAXIS = 3 / number of data axes

NAXIS1 = 5860 / length of data axis 1

NAXIS2 = 3753 / length of data axis 2

NAXIS3 = 3 / length of data axis 3

EXTEND = T / FITS dataset may contain extensions

COMMENT FITS (Flexible Image Transport System) format is defined in 'Astronomy

COMMENT and Astrophysics', volume 376, page 359; bibcode: 2001A&A...376..359H

BZERO = 0. / Offset data range to that of unsigned short

BSCALE = 1. / Default scaling factor

MIPS-HI = 65535 / Lower visualization cutoff

PROGRAM = 'Siril 1.4.0-beta1' / Software that created this HDU

DATE = '2025-05-09T13:08:59' / UTC date that FITS file was created

DATE-OBS= '2025-05-08T23:47:42.297409' / YYYY-MM-DDThh🇲🇲ss observation start,

IMAGETYP= 'Light ' / Type of image

EXPTIME = 180. / [s] Exposure time duration

TELESCOP= 'EQMod Mount' / Telescope used to acquire this image

FILTER = 'mixed ' / Active filter name

FOCALLEN= 371. / [mm] Focal length

XBINNING= 1 / Camera binning mode

YBINNING= 1 / Camera binning mode

XPIXSZ = 5.94999980926514 / [um] Pixel X axis size

YPIXSZ = 5.94999980926514 / [um] Pixel Y axis size

INSTRUME= 'Nikon DSC D750' / Instrument name

STACKCNT= 27 / Stack frames

LIVETIME= 4860. / [s] Exposure time after deadtime correction

EXPSTART= 2460804.46877368 / [JD] Exposure start time (standard Julian date)

EXPEND = 2460804.52934985 / [JD] Exposure end time (standard Julian date)

OBJECT = 'NGC 6888' / Name of the object of interest

SITELAT = 55.0803 / [deg] Observation site latitude

SITELONG= -6.06278 / [deg] Observation site longitude

OBJCTRA = '20 12 26.545' / [H M S] Image center Right Ascension

OBJCTDEC= '+38 26 22.881' / [D M S] Image center Declination

RA = 303.110602250765 / [deg] Image center Right Ascension

DEC = 38.4396891681594 / [deg] Image center Declination

CTYPE1 = 'RA---TAN-SIP' / TAN (gnomic) projection + SIP distortions

CTYPE2 = 'DEC--TAN-SIP' / TAN (gnomic) projection + SIP distortions

CUNIT1 = 'deg ' / Unit of coordinates

CUNIT2 = 'deg ' / Unit of coordinates

EQUINOX = 9.87654321E+107 / Equatorial equinox

CRPIX1 = 1402.346649168 / Axis1 reference pixel

CRPIX2 = 2041.493225096 / Axis2 reference pixel

CRVAL1 = 304.566917223 / [deg] Axis1 reference value

CRVAL2 = 39.2785463087 / [deg] Axis2 reference value

LONPOLE = 180. / Native longitude of celestial pole

CDELT1 = -0.000922019223184954 / [deg] X pixel size

CDELT2 = 0.000922890295645617 / [deg] Y pixel size

PC1_1 = 0.73700202236856 / Linear transformation matrix (1, 1)

PC1_2 = -0.675890537753453 / Linear transformation matrix (1, 2)

PC2_1 = -0.667371954788118 / Linear transformation matrix (2, 1)

PC2_2 = -0.744724562480845 / Linear transformation matrix (2, 2)

A_ORDER = 2 / SIP polynomial degree, axis 1, pixel-to-sky

A_0_0 = 0.

A_1_0 = 0.

A_0_1 = 0.

A_2_0 = 4.626280258975E-07

A_1_1 = -1.7577044651725E-07

A_0_2 = 4.784997371425E-06

B_ORDER = 2 / SIP polynomial degree, axis 2, pixel-to-sky

B_0_0 = 0.

B_1_0 = 0.

B_0_1 = 0.

B_2_0 = 4.511435567025E-07

B_1_1 = -1.17875396549E-06

B_0_2 = 2.7322023604E-06

AP_ORDER= 2 / SIP polynomial degree, axis 1, sky-to-pixel

AP_0_0 = 0.02577049971644

AP_1_0 = -8.59825736312E-06

AP_0_1 = 6.33501074952E-05

AP_2_0 = -4.617817602125E-07

AP_1_1 = 1.9171333336125E-07

AP_0_2 = -4.80917444025E-06

BP_ORDER= 2 / SIP polynomial degree, axis 2, sky-to-pixel

BP_0_0 = 0.0164000465376

BP_1_0 = -5.3930363659E-06

BP_0_1 = 2.32139691131E-05

BP_2_0 = -4.522601131475E-07

BP_1_1 = 1.1903926025275E-06

BP_0_2 = -2.744887354575E-06

HISTORY Crop (x=49, y=135, w=5860, h=3753)

HISTORY Histogram Transf. (mid=0.002, lo=0.050, hi=1.000)

CREATOR = 'ZWO ASIAIR PRO' / Capture software

XORGSUBF= 0 / Subframe X position in binned pixels

YORGSUBF= 0 / Subframe Y position in binned pixels

CCDXBIN = 1 / Camera X Bin

CCDYBIN = 1 / Camera Y Bin

GUIDECAM= 'ZWO ASI120MM Mini' / Guide camera model

ISO = '2500 ' / ISO Value

IMAGEW = 6032 / Image width, in pixels.

IMAGEH = 4032 / Image height, in pixels.

END

 

"On proper polynomial maps of C^n"

Snow Created Ice Cream Sandwich Car Art which created Mandelbrot fractal edges as it melted naturally. It seems like you might be referring to the **Mandelbrot set**, which is associated with fractal mathematics. The Mandelbrot set is defined by the complex quadratic polynomial:

 

\[

z_{n+1} = z_n^2 + c

\]

 

where:

- \( z_n \) is a complex number (initially \( z_0 = 0 \))

- \( c \) is a complex parameter

 

The set comprises all complex numbers \( c \) for which the sequence does not diverge to infinity. Generally, we assess the behavior of the sequence over multiple iterations to determine membership in the Mandelbrot set.

Details about Mandelbrot set is from Google's ChatGPT Sidebar GPT-4o, Claude.

"Polynomials constant on a hyperplane and CR maps of spheres"

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