How to Create the Photon Emission Image

The Tutorial

1. Open a new Excel workbook and create 4 worksheets named: Data, Goal Looker, Chart and Saves unless working from the workbook formerly created, Create a Dakini and Boddhisattva Aspect of the Mother Planet ... ((the Rose worksheet will not be used and neither will EGGIES X and Y). If using that workbook saved under a new name for this article, look for the word NEW or MODIFIED or MODIFIED AGAIN by the Step or Sub-Step (as otherwise all but the last few steps were directly copied and organized into sub-steps). Save the workbook under the filename that makes sense to you in your line of endeavor. The source file for these articles is "Eggies.xlsx".
2. Open Preferences. Recommended Settings: Set General to R1C1 Off and Show the 10 Most Recent Documents; Edit - set all the Top options to checked except Automatically Convert Date System. Display number of decimal places = blank (for integers preferred), Preserve display of dates and set 30 for 21st century cutoff; View - show Formula Bar and status bar, hover for comments and all of Objects, Show gridlines and all boxes below that auto or checked; Chart - show chart names and data markers on hover. Leave rest unchecked for now; Calculation -- Automatically and calculate before save, max change .000,000,000,000,01 w/o commas if you do goal-seeking a lot and save external link values and use 1904 system; Error checking - check all; Save - save preview picture with new files and Save Autorecover after 5 minutes; Ribbon -- all checked except Hide group titles and Developer.
3. Create Defined Name variables:

   1. MODIFIED: In the cell range A1:N1, input the following Variable Names: A1: AjRows; B1: GM (for Golden Mean); C1: Factor1; D1: Factor2; E1: Number; F1: NewDate1; G1: GMSL (for Golden Mean Short Leg); H1: KEY; I1: KEY2_; J1: Variable; M1 Eggies4; N1: ShrinkExpand4
   2. MODIFIED: Select cell range A1:N2 and Insert Name Create (Create Names in) Top Row. Select cell range A2:N2 and do Format Cell Border Outline Center Vertical Center Horizontal Black Bold. Do Format Cell Font Color (fire engine) Red. That is because typically these variables won't be changed.
   3. MODIFIED: In the cell range A3:L3, input the following Variable Names: A3: Tip B3: Base; C3: Spheroids; D3: ShrinkExpand; E3: PiDivisor F3: NewDate2; G3: Base2; H3: Spheroids2; I3: ShrinkExpand2; K3: ShrinkExpand3; L3: Base4
   4. MODIFIED: Select cell range A3:L4 and Insert Name Create (Create Names in) Top Row. Select cell range A4:L4 and do Format Cell Border Outline Center Vertical Center Horizontal Black Bold.. Do Format Cell Font Color (fire engine) Red. That is because typically some of these variables will change but most will not.
   5. Input variable values in row 2: A2: input 2880; Insert New Comment and edit in 2880.
   6. B2: input "=(-(1-SQRT(5))/2)^=(-(1-SQRT(5))/2) ^IF(Spheroids<24,1,1)" and Insert New Comment and edit in "Original formula =(-(1-SQRT(5))/2)^=(-(1-SQRT(5))/2) ^IF(Spheroids<24,1,1)"
   7. MODIFIED AGAIN: C2: input "=VLOOKUP(ABS(Spheroids),LOOKER,IF(Spheroids<=24,2,2))" and do Insert New Comment and edit in "Original formula was =VLOOKUP(ABS(Spheroids),LOOKER,IF(Spheroids<=24,2,3)) and now is =VLOOKUP(ABS(Spheroids),LOOKER,IF(Spheroids<=24,2,2))"
   8. MODIFIED: D2: Input "=VLOOKUP(ABS(Spheroids),LOOKER,IF(Spheroids<=24,2,2))" and Do Insert New Comment and edit in "Original formula =VLOOKUP(ABS(Spheroids),LOOKER,IF(Spheroids<=24,2,2))"
   9. E2: Input 1. This variable, Number, is not being used at present. It's purpose is to warp or skew the output via incorporation into the formulas in cell range C6:I2886. Insert a New Comment if you like.
   10. F2: Input "=1954/9/2". This variable, NewDate1, is not being used at present. It's purpose is to warp or skew the output personally via incorporation into the formulas in cell range C6:I2886. It is a birth date in format yyyy/mm/dd, i.e. a double quotient. Insert a New Comment if you like.
   11. G2: Input "=1-(-(1-SQRT(5))/2)^IF(Spheroids<24,1,1)" and Do Insert New Comment and edit in "Original formula =1-(-(1-SQRT(5))/2)^IF(Spheroids<24,1,1)"
   12. MODIFIED AGAIN: H2: Input "=IF(Spheroids>=30,Spheroids*5/5,Spheroids)" w/o the quotes. Insert New Comment and edit in "Keeps Spheroids round. Formula was =IF(Spheroids>=30,Spheroids/30,Spheroids) now is =IF(Spheroids>=30,Spheroids*5/5,Spheroids)". Expand the comment frame if need be.
   13. MODIFIED: I2: Input "=IF(Spheroids>=30,Spheroids,Spheroids2)" w/o the quotes. Insert New Comment and edit in "Keeps Spheroids2 round. New formula is =IF(Spheroids>=30,Spheroids,Spheroids2)". Expand the comment frame if need be.
   14. NEW: In J2, enter 1.
   15. MODIFIED AGAIN: In M2, enter 100.
   16. NEW: In N2, enter 1
4. Omitting this step and sub-steps: Select cell R8 and enter LOOKER2 for the entry of that table. Had to do with old formulation of KEY. Also omitting section to do with Rose worksheet further down.
5. Save the workbook.
6. Input variable values in row 4:

   1. A4: input "=Base*12/(VARIABLE/1)*PI()"; Insert New Comment and edit in "Original formula =Base*12/(VARIABLE/1)*PI()". Expand the comment frame if need be.
   2. B4: Input "=16*107". Insert New Comment and edit in "Original constant value =16*107."
   3. MODIFIED AGAIN: C4: Input 1000. Do Insert New Comment and edit in comment "See Lookup Tables for range of Spheroids values contemplated by this worksheet. Was 100. Now is 1000." Expand the comment frame if need be. See Tips for variations.
   4. D4: Input 1. Do Insert New Comment and edit in comment "Input 1 if keeping input data for Spheroids normalized, else 2 to shrink by 1/2, or .5 to expand by a factor of 2, since ShrinkExpand is a Divisor." Expand the comment frame if need be.
   5. E4: Input 180. Do Insert New Comment and edit in comment "Normally this will not be changed from 180, but can be for warping effects. Original value 180". Expand the comment frame if need be.
   6. F4: Input "=(1958/4/13)". This variable, NewDate2, is not being used at present. It's purpose is to warp or skew the output personally via incorporation into the formulas in cell range C6: I2886. It is a birth date in format yyyy/mm/dd, i.e. a double quotient. Insert a New Comment if you like.
   7. G4: Input "=16*107". Insert New Comment and edit in "Original constant value =16*107."
   8. MODIFIED AGAIN: H4: Input 30 . Insert New Comment and edit in "=Spheroids is original formula because most often Spheroids2 is the Standard or Goal for Spheroids, and needs to correspond per period on a 1:1 basis. Was 40. Was 12. Now 30." Expand the comment frame if need be.
   9. MODIFIED AGAIN: I4: Input 1. Insert New Comment and edit in "Original formula =ShrinkExpand is most usual value as Standard or Goal, e.g. 100% of Normal. But if 80% of Normal is the New Goal, say for a Personal Fitness Program, then a little math is required.  ShrinkExpand2 = 1/.80, or 1.25 would be the new input. This is because it was thought the natural trend would be to want to shrink by say a factor of 2, so 2 = 1/.50 and the New Goal is to be 50% of Normal, or shrink by a factor of 2 (as a divisor). You may change the formulas and comments so that ShrinkExpand and ShrinkExpand2 are multiplicative instead of divisive if preferred. Was 1.19122798149309. Was =(1/E2890)^(3/2). Now = 1." Expand the comment frame if need be. In cell E2890 should be the formula "=MAX(E6:E2886)"and above it the MIN formula.
   10. K4: Input 0.9 and Insert New Comment with this value as what's now current if you prefer.
   11. NEW: L4: Input "=16*107"
7. MODIFIED: Input the Column Headings across row 5. A5: Base t; B5: c; C5: Cos; D5: Sin; E5: Main X; F5: Main Y; G5: Count2; H5: Second X; I5: Second Y; J5: Rose X; K5: Rose Y; L5: Count4; M5: EGGIES X; N5: EGGIES Y. Select cell range A5:I5 and Format Cell Font Underline. Select the following cells with Shift+Command: C4, D4, F4. G4, H4, I4, K4, L4, J2, M2, N2 and Format Cell Fill canary yellow (for input cells) and Font size 14. Format Cells A4:L4 Number Number Decimal Places 4 and select column range A:N and do Format Column Autofit Selection.
8. Save the workbook.
9. Enter the columnar formulas:

   1. Cell A6: Input "=IF(ODD(Spheroids)=Spheroids,0,Tip)" and do Insert Comment and edit comment "Original formula =IF(ODD(Spheroids)=Spheroids,0,Tip)". Expand the comment frame if need be. Do Format Cell Fill Light Rose color to distinguish it from the other cells in the column.
   2. MODIFIED: Edit Go To cell range A7:A2886 and with A7 the active high-lighted cell, input "=(A6+(-Tip*2)/(AjRows))" and do Edit Fill Down. Select cell A7 and copy the the formula in the formula bar and do Insert New Comment and edit comment "Original formula "=(A6+(-Tip*2)/(AjRows)) to bottom A2886 (as adjusts per cell on the way down)". Expand the comment frame if need be.
   3. MODIFIED: Cell B6: Input "=IF(Spheroids<=24, Base*24/Spheroids,Base*24/Spheroids) and do Insert New Comment "Original formula is really =Base*24/Spheroids"
   4. Edit Go To cell range B7:B2886 and with B7 the active high-lighted cell, input "=B6" and do Edit Fill Down. Select cell B7 and copy the the formula in the formula bar and do Insert New Comment and edit comment "Original formula =B6 to bottom B2886 (as adjusts per cell on the way down)". Expand the comment frame if need be.
   5. Edit Go To cell range C6:C2886 and with C6 the active high-lighted cell input "=Spheroids/KEY*(COS((ROW()-6)*Number*PI()/PiDivisor*Factor1))" and do Edit Fill Down. Select cell C6 and do Insert New Comment and edit it "Original Formula =Spheroids/KEY*(COS((ROW()-6)*Number*PI()/PiDivisor*Factor1))". Expand the comment frame if need be. This formula and the next one form the ring the Spheroids occupy, By taking the cosine of the cell 6 rows above the cell it's in, C6, the formula is taking the cosine of 0, which = 1.
   6. MODIFIED: Edit Go To cell range D6:D2886 and with D6 the active high-lighted cell input "=Spheroids/KEY*(SIN((ROW()-6)*Number*PI()/PiDivisor*Factor1))" and do Edit Fill Down. Select cell D6 and do Insert New Comment and edit it "Original Formula =Spheroids/KEY*(SIN((ROW()-6)*Number*PI()/PiDivisor*Factor1)). By taking the sine of the cell 6 rows above the cell we're in, C6, the formula is taking the sine of 0, which = 0. Therefore, between the formula in C6 and the one in D6, the {x,y} coordinates of the first cell would be {1,0} if nothing else were affecting them. It proceeds counterclockwise from there. so that is how to read the chart, from 0 degrees counter clockwise back to 360 degrees. Even though there are basically 2880 rows being charted, and 2880/360 = 8, the factor = 1/8th at .125, so a level of detail is achieved while keeping everything normalized for a single cycle in the typical case.
   7. Edit Go To cell range E6:E2886 and with E6 the active high-lighted cell, input the formula, "=((SIN(A6/(B6*2))*GM*COS(A6)*GM*(COS(A6/(B6*2)))*GM)+C6)*VLOOKUP(ROW(),SpreadLooker,3)/ShrinkExpand" w/o quote marks and do Edit Fill Down. Select cell E6 and do Insert New Comment "Original Formula =((SIN(A6/(B6*2))*GM*COS(A6)*GM*(COS(A6/(B6*2)))*GM)+C6)*VLOOKUP(ROW(),SpreadLooker,3)/ShrinkExpand multiplies each term of the standard formula for a spherical helix per 'CRC Standard Curves and Surfaces' by David von Seggern, 1993, by GM (Golden Mean) to keep things proportional, with the z dimension added into the x and y dimensions. This is then multiplied by the Lookup Table SpreadLooker, which either randomizes the data or accepts inputs per the Goal Looker worksheet. Lastly, it is subject to ShrinkExpand, a variable for normalizing or growing or shrinking its chart relative to the Standard or Goal chart data series of Second X and Second Y." Expand the comment frame as much as necessary. I realize that there will be #NAME? error values -- these will be fixed in a little while.
   8. Edit Go To cell range F6:F2886 and with F6 the active high-lighted cell, input the formula,"=((SIN(A6/(B6*2))*GM*SIN(A6)*GM*(COS(A6/(B6*2)))*GM)+D6)*VLOOKUP(ROW(),SpreadLooker,3)/ShrinkExpand" w/o quote marks and do Edit Fill Down. Select cell F6 and do Insert New Comment "Original Formula =((SIN(A6/(B6*2))*GM*SIN(A6)*GM*(COS(A6/(B6*2)))*GM)+D6)*VLOOKUP(ROW(),SpreadLooker,3)/ShrinkExpand (see note in E6 for details)." I realize that there will be #NAME? error values -- these will be fixed in a little while.
   9. MODIFIED: Cell G6: Input "=IF(Spheroids2
   10. Edit Go To cell range G7:G2886 and with G7 the active high-lighted cell, input the formula,"=G6". Do Insert New comment and edit in "Original Formula =G6 down to G2886 as adjusts per cell thereto."
   11. MODIFIED AGAIN: Edit Go To cell range H6:H2886 and with H6 the active high-lighted cell, input the formula,"=((SIN(A6/(G6*2))*GM*COS(A6)*GM*(COS(A6/(G6*2)))*GM)+C6)/ShrinkExpand2" w/o quotes and Edit Fill Down. Do Insert Comment and edit comment "Original formula =((SIN(A6/(G6*2))*GM*COS(A6)*GM*(COS(A6/(G6*2)))*GM)+Spheroids2/KEY2_*(COS((ROW()-6)*Number*PI()/PiDivisor*Factor2)))/ShrinkExpand2 is now =((SIN(A6/(G6*2))*GM*COS(A6)*GM*(COS(A6/(G6*2)))*GM)+C6)/ShrinkExpand2 with ShrinkExpand2 being the Goal or Standard the Spheroids of Main X and Main Y are to attain." See original Step 25 for notes on ShrinkExpand2. Expand the comment frame if need be.
   12. MODIFIED AGAIN: Edit Go To cell range I6:I2886 and with I6 the active high-lighted cell, input the formula,"=((SIN(A6/(G6*2))*GM*SIN(A6)*GM*(COS(A6/(G6*2)))*GM)+D6)/ShrinkExpand2" w/o quotes and Edit Fill Down. Do Insert Comment and edit comment "Original formula =((SIN(A6/(G6*2))*GM*SIN(A6)*GM*(COS(A6/(G6*2)))*GM)+Spheroids2/KEY2_*(SIN((ROW()-6)*Number*PI()/PiDivisor*Factor2)))/ShrinkExpand2 is now =((SIN(A6/(G6*2))*GM*SIN(A6)*GM*(COS(A6/(G6*2)))*GM)+D6)/ShrinkExpand2 with ShrinkExpand2 being the Goal or Standard the Spheroids of Main X and Main Y are to attain." See original Step 25 for notes on ShrinkExpand2.Expand the comment frame if need
10. Save the Workbook. Enter the remaining Lookup Tables, starting with LOOKER on the Data worksheet:

    1. Edit Go To cell range  O6:O2886 and with O6 the active cell, enter 1. Do Edit Fill Series Columns Linear Step Value 1 OK. Select cell O5 and type LOOKER.
    2. MODIFIED: Edit Go To cell Range P6:P2886 and with P6 the active cell, enter .125 and then do Edit Fill Down. Select P5 and type Std. 1/8th
    3. Edit Go To cell range Q6:Q2886 and with Q6 the active high-lighted cell, enter the formula, "=O6*$Q$35/$O$35" and do Edit Fill Down. Select cell Q35 and input .125; Select cell Q5 and type Relative. Select cell Q6 and do Insert New Comment and edit in "Original formula =O6*$Q$35/$O$35 with .125 in Q35."
    4. Edit Go To cell range O6:Q2886 and Insert Name Define LOOKER to range $O$6:$Q$2886. Format Cells Border (fire engine) Red Bold Outline.
11. Now enter the SpreadLooker table:

    1. Select cell U5 and input 1.
    2. Select cell W1 and type DIVIDED BY. Select cell W2 and Insert Define Name as DIVIDED_BY and Format Cells Border Outline Black.
    3. Select cell W2 and input 1. Do Insert Comment and edit comment "Try .25 or .5 when Lookup Table fully operational -- playing with this idea -- not settled yet. Entering a 6 leads to beginning of chaos! Has to do with Phases?" Inputting .6 in the current circumstances leads to rows>2880 but the design is not so great.
    4. MODIFIED: Select cell U6 and input the formula, "=(6+AjRows/(Spheroids))/DIVIDED_BY". Do Insert New Comment and edit in "Original formula =(6+AjRows/(Spheroids))/DIVIDED_BY. So, in the case of 24 Spheroids and 2880 AjRows, 2880/24 = 120 + 6 = 126. The original Vlookup formula finds which row() it's currently in and compares it to this number, thus bracketing the data (spheroids) into groups (of rows)."
    5. MODIFIED: Select cell U4 and enter formula "=U6-6" w/o quotes. Do Insert New Comment and edit in "Original formula =U6-6." Insert Name Define Increment for cell $U$4. Do Format Cells Number Custom "Increment "0 and double click the U column header's right divider line to auto-adjust to fit. Format Font 14 red and Border Blue bold Outline.
    6. MODIFIED: Edit Go To cell range U7:U64 and with U7 the active high-lighted cell, enter the formula, "=Increment+U6" and do Edit Fill Down. Do Insert New Comment and edit in "Original formula =Increment+U6"
    7. Select cell V4 and type SpreadLooker. Format Cells Fill canary yellow Font fire engine Red Bold.
    8. Enter 1 into cell V5.
    9. MODIFIED: Edit Go To cell range V6:V64 and with V6 the active high-lighted cell, enter the formula, "=Spheroids-IF((Spheroids-(ROW()-5))>0,(Spheroids-(ROW()-5)),0)" and do Edit Fill Down. Do Insert New Comment and edit in "Original formula =Spheroids-IF((Spheroids-(ROW()-5))>0,(Spheroids-(ROW()-5)),0) which will progress in a step value of 1 until the number of Spheroids is reached and then repeat that number."
    10. Select cell W4 and type Spreader.
    11. MODIFIED: Edit Go To cell range W5:W64 and with cell W5 active and high-lighted, enter the formula, "=VLOOKUP(V5,Goal_Looker_Eggbasket,2)" and do Edit Fill Down. Do Insert New Comment and edit in "Original formula =VLOOKUP(V5,Goal_Looker_Eggbasket,2), i.e. it will look up the Spheroid number from column V here and then go on the Goal Looker worksheet's #2 B column of the Defined Range 'Goal_Looker_Eggbasket' there in cells A2:C65 matching that Spheroid number -- i.e. it will return a unique (random?) value per Spheroid for the number of Spheroids the user has input."
    12. Select cell X4 and type Eggbasket.
    13. MODIFIED: Edit Go To cell range X5:X64 and with cell X5 active and high-lighted, enter the formula,"=VLOOKUP(V5,Goal_Looker_Eggbasket,3)" and do Edit Fill Down. Do Insert New Comment and edit in "Original formula =VLOOKUP(V5,Goal_Looker_Eggbasket,3), i.e. it will lookup the Spheroid number from column V here and then go on the Goal Looker worksheet's #3 C column of the Defined Range 'Goal_Looker_Eggbasket' there in cells A2:C65 matching that Spheroid number -- i.e. it will return a unique (random?) value per Spheroid for the number of Spheroids the user has input. This (random?) value will be returned to Main X and Main Y."
    14. Edit Go To cell range U5:X105 and Insert Define Name  SpreadLooker to cell range $U$5:$X$64.
    15. MODIFIED: Do Format Cells Fill sky blue. Select cell U6 and do Format Cells Fill color rosy red and font red because the formula is different from the others in the column.
    16. Select cell range W5:X64 and Format Cells Number Decimal Places 2.
12. Activate or create a new worksheet Goal Looker if not already done.

    1. MODIFIED: Input the Column Headings. A1: RANGE; B1: Pasted VAL; C1: EggBasket; D1: RandBetween; E1: Spiral. Select columns A:E and do Format Column Autofit Selection, Format Cells Number 2 decimal places OK.
    2. MODIFIED: Edit Go To cell range A2:C65 and Insert Name Define  Goal_Looker_Eggbasket  to cell range $A$2:$C$65.
    3. Edit Go To cell range A2:A65 and with A2 the active high-lighted cell, input 1, then do Edit Fill Series Columns Linear Step Value 1 OK.
    4. MODIFIED AGAIN: Copy column B's contents to a safe empty column for now. Edit Go To E2:E65 and input 1.5 into cell E2 and do shift+tab and input 0 into cell E65 and do Edit Fill Series Column accept the proposed Step Value OK. Copy these values and do Paste Special Values into cell range B2:B65 to see the large spiral effect on the chart. You may notice that since there are 24 divisions of 2880 due to 24 typically being the number of Spheroids, that if you look across from 24 in column B or E that the last value is .95, not the bottom value of 0. It's possible to do Insert New Comment about this at the top on the label Spiral or in the first active formula cell.
13. Check for errors; there should be none. To get a good chart, columns E:I of the Data worksheet should be error-free. See the Warnings section below for help in errors reduction.

Explanatory Charts, Diagrams, Photos

1. (dependent upon the tutorial data above)

1. Create the Chart.

   1. MODIFIED: Activate Data worksheet and Edit Go To cell range H6:I2886. Either do Chart Wizard or select Chart on the Ribbon (activated in Preferences) and select All, Scattered, Smoothed Line Scattered. If using Chart Wizard, a new Chart worksheet will be created. Otherwise, copy or cut and paste the chart into the upper left corner of the Chart worksheet you created at the beginning, and hover the mouse over the lower right corner until it becomes a double-headed arrow and then use it to pull the chart into an expansion of a large Square. Format Selection Heavier Dashed Line and Line Weight 1 and Leaf Green (to the yellow) from the color table, transparency 0%. This is the main surrounding ring.
   2. MODIFIED: On the Chart worksheet, do menuitem Chart Add Data. In response to the Range request, activate the Data worksheet again and Edit Go To cell range E6:F2886. When I do it, it does not work right and it takes another column instead of column E. Click on the second standard ring series, or double-click until it appears in the formula bar and edit it until it reads as follows: =SERIES(,Data!$E$6:$E$2886,Data!$F$6:$F$2886,2). Edit the line of Series 2 to be solid and 1 point line weight and Dark Blue in hue. It has a very heavy 8 pt yellow 25% transparent glow w/o soft edges. This is the bright glowing emitted photon.
   3. Any other series which Excel creates should be deleted by clicking on it and deleting it from the Formula Bar.
   4. Double-click on the Plot Area and set the Gradient to be Radial, Centered, Teal Blue on far right and Dark Purple on far left. I have No Line set for either the Plot Area or the Chart Area, no Chart Titles, No Axes which are all controlled by Chart Layout (which appears on the Ribbon when you click on the Chart Plot Area). The Chart Area color is Teal Blue.
   5. Copy the formulas  from A1:X64 to the Saves worksheet and then, below the formulas, paste them again, and then do Paste Special Values right over them. Then with the shift key held down, tale a picture of the chart under each of the two series definitions, Pasting Pictures with the shift key depressed into the Saves worksheet under the data.
   6. Save the workbook.

2. Photon Emission Image

Helpful Guidance

1. Make use of helper articles when proceeding through this tutorial:

   1. See the article How to Create a Spirallic Spin Particle Path or Necklace Form or Spherical Border for a list of articles related to Excel, Geometric and/or Trigonometric Art, Charting/Diagramming and Algebraic Formulation.
   2. For more art charts and graphs, you might also want to click on Category:Microsoft Excel Imagery, Category:Mathematics, Category:Spreadsheets or Category:Graphics to view many Excel worksheets and charts where Trigonometry, Geometry and Calculus have been turned into Art, or simply click on the category as appears in the upper right white portion of this page, or at the bottom left of the page.