How to Create Art from Trig Like Cherries in a Bowl
Three Parts:The TutorialExplanatory Charts, Diagrams, PhotosHelpful Guidance
You will learn how, in Microsoft Excel, to create art from trigonometry like the following image of 'Cherries in a Bowl', but please read the Warnings Section on Processor Time before proceeding.
Part 1 The Tutorial
 1Create a new Excel workbook with 3 worksheets: Data01, Saves and Chart (unless you are working with Chart Wizard). Select your image you want to make art from trigonometry by  here, for example, the objective is a bowl of cherries. Decide on the basic curve to employ. Here, for example, the curve selected was the sine wave curve on a sphere because it can come to inner endpoints like a cherry does, also because of shading considerations it's better than the spherical helix and finally because of the way spheres are joined, the stems are not spirallic as in the spherical helix. The basic plan is to make random arrangements of cherries in a bowl that may fluctuate at the user's discretion, so that the user may choose the arrangement they find most pleasing. The selection here represented had stems that were too long, and there has been a significant Revision from the chart data via inspection of where the 1's occur in column D, especially concerning "twinned cherries"  look for MODIFIED or NEW if you are revising your work to date please. This workbook is very timeintensive and a lot of effort is being made to obtain the best results possible.
 2Set Your Preferences. Open Preferences in the Excel menu and follow the directions below for each tab/icon.
 In General, set R1C1 to Off and select Show the 10 Most Recent Documents .
 In Edit, set all the first options to checked except Automatically Convert Date System. Set Display number of decimal places to blank (as integers are preferred). Preserve the display of dates and set 30 for 21st century cutoff.
 In View, click on show Formula Bar and Status Bar and hover for comments of all Objects . Check Show gridlines and set all boxes below that to auto or checked.
 In Chart, allow Show chart names and set Data markers on hover and leave the rest unchecked for now.
 In Calculation, Make sure Manually is checked and Calculate before save is not checked. Set max change to .001 without commas as goalseeking is not done a lot. Check Save external link values and Use 1904 system
 In Error checking, check all the options.
 In Save, select Save preview picture with new files and Save Autorecover after 5 minutes
 In Ribbon, keep all of them checked except Hide group titles and Developer .
 3It helps by placing the cursor at cell A16 and doing Freeze Panes. Edit Go To cell range A1:R17292 and Format Cells Number Number Decimal Places 4, Font Size 9 to 12. Fill (from the color wheel) range A1:R17288 a nice fuchsia and make the Border Dark Blue bold Outline.
 4Enter the upper Defined Name Variables Section (here's a picture):
 Select cell range A1:F3 and Format Fill white. Enter to cell A1, aligned left, Sinewave Spheres as Cherries in a Bowl and make Font red and Fancy, such as Apple Chancery, perhaps, size 14.
 G1: Enter AYE; G2: Enter BEE; G3: Enter CEE. Format Font size 14 bold.
 H1: Enter 20; H2: Enter .50; H3: Enter .50 and Format Fill yellow (to indicate these are input cells). Select cell range G1:H3 and Insert Name Create Names in Left Column, OK. Format G1:H3 Border Navy Blue bold Outline with Tops and Bottoms of cells bordered, but not the center divider. Copy cell range G1:H3 to I1, K1, M1, O1 and Q1. Select G1:R3 and Format Alignment Horizontal Center and Format Cell Number Number Decimal Places 2.
 I1: Enter Stretch_x1; I2: Enter Stretch_y1; I3: Enter SHRINKER.
 J1: Enter w/o quotes "=(8.5*(SHRINKER*10))"; J2: Enter w/o quotes "=(8.5*(SHRINKER*10))"; J3: Enter w/o quotes "=0.1*12/SPHERES". Select Cell Range J1:J3 and Format Fill white (to indicate these are noninput formulaic variables). Select cell range I1:J3 and Insert Name Create Names in Left Column, OK.
 K1: Enter ROWS; K2: Enter MAGIC; K3: Enter SPHERES and Format Cell font 16 bold format fill sky blue.
 L1: Enter"=172855"; L2: Enter "=ROUND(ROWS/SPHERES,0)"; L3: Enter 18 for now and format fill L3 yellow. Although the number of "cherries" can go higher, they shrink and their stems grow way too long as their numeric volume increases, so 20 is about the upper limit. Format Fill L1:L2 white. Select cell range K1:L3 and Insert Name Create Names in Left Column, OK.
 M1: Enter AYE2_ and bold the font; M2: Enter Magic2; M3: Enter SWS2_ (for SineWave Spheres 2) and make the font bold size 16, and format fill sky blue.
 MODIFIED: N1: Enter 20 and format fill yellow; N2: Enter w/o quotes "=ROUND(ROWS/SWS2_,0)" and format fill white; N3: enter 15 for now and Format Fill yellow. Select cell range M1:N3 and Insert Names Create Names in Left Column, OK.
 O1: Enter Stretch_x2; O2: Enter Stretch_y2; O3: Enter Shrinker2.
 P1: Enter w/o quotes "=Stretch_y2"; P2: Enter w/o quotes "=(8.5*(Shrinker2*10))"; P3: Enter w/o quotes "=0.1*12/SWS2_". Select cell range P1:P3 and Format Fill white. Select cell range O1:P3 and Insert Name Create Names in Left Column, OK.
 Q1: Enter Factor and make bold; Q2: Enter FactorUpY; Q3: Enter FactorUpX
 R1: Enter w/o quotes "=3/15*SWS2_"; R2: Enter w/o quotes "=SWS2_/15*0.9"; R3: Enter w/o quotes "=IF(SWS2_/15>=1.5,SWS2_/15*2/3,SWS2_/15)". Select cell range R1:R3 and Format Fill white. Select cell range Q1:R3 and Insert Name Create Names in Left Column, OK.
 5Enter the column heading of rows 4 and 5
 A5: Adj Cos; B5: Adj Sin
 C5: Indicator; D5: Indicator2 (These two columns, esp. D, indicate where new sphere or cherry starts and old ones end, so they indicate where the connecting lines (stems) are over in the charting columns. These connecting lines may be verified by hovering over them on the chart with the cursor until the datapoint data appears. It's a good opportunity for a macro to be written to handle deleting the connector cells).
 E5: t2: 0 to nπ; F5: z2_
 G5: t: 0 to nπ; H5: z1_
 I5: Adj_x1; J5: Adj_y1
 K4 and L4: Charting; K5: x: No z; L5: y: With z and select K4:L5 and do Format Font bold italic.
 M5: Randy_x; N5: Randy_y
 O5: Adj_x2; P5: Adj_y2
 Q4 and R4: Charting; Q5: x2: No z; LR5: y2: With z and select Q4:R5 and do Format Font bold italic.
 NEW: S5 and T5: IF D8, IF D7
 NEW: U5: AvgNNx and V5: AvgNNy
 NEW: W5: MAX. Align S5:W5 horizontally centered.
 6Enter the column formulas
 Edit Go To A6:A17285 and enter to A6 "=17*COS((ROW()6)*0.25/12*PI()/180)" w/o quotes and Edit Fill Down.
 Edit Go To B6:B17285 and enter to B6 "=17*SIN((ROW()6)*0.25/12*PI()/180)+17" w/o quotes and Edit Fill Down.
 Select cell C6 and enter 1. Edit Go To C7:C17285 and enter to C7 "=IF((ROW()7)/MAGIC=INT((ROW()7)/MAGIC),1,IF((ROW()7)=0,1,0))" w/o quotes and Edit Fill Down.
 Select cell D6 and enter 1. Edit Go To D7:D17285 and enter to D7 "=IF((ROW()7)/Magic2=INT((ROW()7)/Magic2),1,IF((ROW()7)=0,1,0))" w/o quotes and Edit Fill Down.
 Go to E6 and enter 0. Go to E7 and enter w/o quotes "=(2*PI()/Magic2)". Edit Go To E8:E17285 and enter to E8 "=IF(D8=1,2*PI(),2*PI()/Magic2+E7)" w/o quotes and Edit Fill Down.
 Edit Go To F6:F17285 and enter to F6 "=CEE*COS(AYE2_*E6)" w/o quotes and Edit Fill Down. Insert Name Define Name z2_ to cell range $F$6:$F$17285.
 Go to G6 and enter 0. Go to G7 and enter w/o quotes "=(2*PI()/MAGIC)". Edit Go To G8:G17285 and enter to G8 "=IF(C8=1,2*PI(),2*PI()/MAGIC+G7)" w/o quotes and Edit Fill Down.
 Edit Go To H6:H17285 and enter to H6 "=CEE*COS(AYE*G6)" w/o quotes and Edit Fill Down. Insert Name Define Name z1_ to cell range $H$6:$H$17285.
 Edit Go To I6:I17285 and enter to I6 "=IF(C6=1,A6,I5)" w/o quotes and Edit Fill Down. Insert Name Define Name Adj_x1 to cell range $I$6:$I$17285.
 Edit Go To J6:J17285 and enter to J6 "=IF(C6=1,B6,J5)" w/o quotes and Edit Fill Down. Insert Name Define Name Adj_y1 to cell range $J$6:$J$17285.
 Edit Go To K6:K17285 and enter to K6 "=SHRINKER^2*(Stretch_x1*(((BEE^2CEE^2*COS(AYE*G6)*COS(AYE*G6))^0.5*COS(G6)))+Adj_x1)" w/o quotes and Edit Fill Down.
 Edit Go To L6:L17285 and enter to L6 "=SHRINKER^2*(Stretch_y1*(((BEE^2CEE^2*COS(AYE*G6)*COS(AYE*G6))^0.5 *SIN(G6))+z1_)+Adj_y1)" w/o quotes and Edit Fill Down.
 Edit Go To M6:M17285 and enter to M6 "=RANDBETWEEN(4,4)/1" w/o quotes and Edit Fill Down. Insert Name Define Name Randy_x to cell range $M$6:$M$17285.
 Edit Go To N6:N17285 and enter to N6 "=RANDBETWEEN(0,25)/10" w/o quotes and Edit Fill Down. Insert Name Define Name Randy_y to cell range $N$6:$N$17285.
 Edit Go To O6:O17285 and enter to O6 "=IF(D6=1,A6*Randy_x/10*Factor,O5)" w/o quotes and Edit Fill Down. Insert Name Define Name Adj_x2 to cell range $O$6:$O$17285.
 Edit Go To P6:P17285 and enter to P6 "=IF(D6=1,B6*Randy_y/10*Factor*2,P5)" w/o quotes and Edit Fill Down. Insert Name Define Name Adj_y2 to cell range $P$6:$P$17285.
 MODIFIED: Delete entries in cell range Q6:R7. Edit Go To Q8:Q17285 and enter to Q8 "=IF(D8=1,VLOOKUP(W8,D_Looker,2),IF(S8="B",Q7,(Shrinker2^2*(Stretch_x2*(((BEE^2CEE^2*COS(AYE2_*E8)*COS(AYE2_*E8))^0.5 *COS(E8)))+Adj_x2)*FactorUpX)))" w/o quotes and Edit Fill Down.
 MODIFIED: Edit Go To R8:R17285 and enter to R8 "=IF(D8=1,VLOOKUP(W8,D_Looker,3),IF(T8="B",R7,(Shrinker2^2*(Stretch_y2*(((BEE^2CEE^2*COS(AYE2_*E8)*COS(AYE2_*E8))^0.5 *SIN(E8))+z2_)+Adj_y2)*FactorUpY)))" w/o quotes and Edit Fill Down.
 NEW: Edit Go To S8:S17285 and enter to S8 w/o external quotes the formula "=IF(D8=1,(Shrinker2^2*(Stretch_x2*(((BEE^2CEE^2*COS(AYE2_*E8)*COS(AYE2_*E8))^0.5*COS(E8)))+Adj_x2) *FactorUpX),IF(D7=1,"B",""))"
 NEW: Edit Go To T8:T17285 and enter to T8 w/o external quotes the formula "=IF(D8=1,(Shrinker2^2*(Stretch_y2*(((BEE^2CEE^2*COS(AYE2_*E8)*COS(AYE2_*E8))^0.5*SIN(E8))+z2_)+Adj_y2)* FactorUpY),IF(D7=1,"B",""))"
 NEW: Edit Go To U2886 and enter and center Avg01x and go to V2886 and enter and center Avg01y. Go to U2887 and enter w/o quotes "=AVERAGE(S8:S2887)" and go to V2887 and enter w/o quotes "=AVERAGE(T8:T2887)". Select cell range U2886:V2887 and Insert Name Create Names in Top Row, OK.
 NEW: Edit Go To U5766 and enter and center Avg02x and go to V5766 and enter and center Avg02y. Go to U5767 and enter w/o quotes "=AVERAGE(S2888:S5767)" and go to V5767 and enter w/o quotes "=AVERAGE(T2888:T5767)". Select cell range U5766:V5767 and Insert Name Create Names in Top Row, OK.
 NEW: Edit Go To U8646 and enter and center Avg03x and go to V8646 and enter and center Avg03y. Go to U8647 and enter w/o quotes "=AVERAGE(S5768:S8647)" and go to V8647 and enter w/o quotes "=AVERAGE(T5768:T8647)". Select cell range U8646:V8647 and Insert Name Create Names in Top Row, OK.
 NEW: Edit Go To U11526 and enter and center Avg04x and go to V11526 and enter and center Avg04y. Go to U11527 and enter w/o quotes "=AVERAGE(S8648:S11527)" and go to V11527 and enter w/o quotes "=AVERAGE(T8648:T11527)". Select cell range U11526:V11527 and Insert Name Create Names in Top Row, OK.
 NEW: Edit Go To U14406 and enter and center Avg05x and go to V14406 and enter and center Avg05y. Go to U14407 and enter w/o quotes "=AVERAGE(S11528:S14407)" and go to V14407 and enter w/o quotes "=AVERAGE(T11528:T14407)". Select cell range U14406:V14407 and Insert Name Create Names in Top Row, OK.
 NEW: Edit Go To U16326 and enter and center Avg06x and go to V16326 and enter and center Avg06y. Go to U16327 and enter w/o quotes "=AVERAGE(S14408:S16327)" and go to V16327 and enter w/o quotes "=AVERAGE(T14408:T16327)". Select cell range U16326:V16327 and Insert Name Create Names in Top Row, OK.
 NEW: Edit Go To U17284 and enter and center Avg07x and go to V17284 and enter and center Avg07y. Go to U17285 and enter w/o quotes "=AVERAGE(S16328:S17285)" and go to V17285 and enter w/o quotes "=AVERAGE(T16328:T17285)". Select cell range U17284:V17285 and Insert Name Create Names in Top Row, OK.
 NEW: Go to cell D17285 and directly overwrite the formula with a 1 and format fill yellow with font red and bold, size 14.
 NEW: Unfreeze panes and refreeze at A20.
 NEW: Go to W7 and enter w/o quotes the formula "=IF(D7=1,1,0)". Edit Go To W7:W17285 and enter to W7 w/o quotes the formula "=IF(D8=1,MAX($W$6:W7)+1,W7)" and Edit Fill Down.
 NEW: Edit Go To cell range X1 to X19 and enter to X1 the formula w/o quotes "=(Magic2*ROW())+7" and Edit Fill Down.
 7NEW: Enter the D_Looker vlookup table:
 NEW: Edit Go To cell range Y1:Y19 and enter 1 to Y1 and do Edit Fill Series Columns Linear Step Value = 1, OK.
 NEW: Z1: Enter "=Avg01x" and AA1 enter "=Avg01y" and copy Z1:AA1 and paste to Z2:AA4. Edit the formulas in Z4 and AA4 to read "=Avg02x" and "=Avg02y" and copy these to Z5:Z7. Edit the formulas in Z7 and AA7 to read "=Avg03x" and "=Avg03y" respectively and copy these to Z8:AA10. Edit the formulas in Z10 and AA10 to read "=Avg04x" and "=Avg04y" and copy these and paste them to Z11:AA13. Edit the formulas in Z13 and AA13 to read "=Avg05x" and "=Avg05y" respectively and copy these and paste them to Z14:AA16. Edit the formulas in Z16 and AA16 to read "=Avg06x" and "Avg06y" and copy these and paste them to Z17:AA19. Edit the formulas in Z19 and AA19 to read "=Avg07x" and =Avg07y", respectively.
 Select Y1:AA19 and Insert Name Define Name D_Looker to cell range $Y$1:$AA$19.
 8It is much faster to have a minichart of columns Q and R with red line, weight 1, on the DATA01 worksheet than to wait the 5 minutes for the actual chart to generate.
 Command+Shift Select K6:L17288 and Q6:R17288 and Format Fill sky blue for the charting columns.
 Select K17286 and enter w/o quotes "=K6" to make the complete connecting line. Format fill sea foam green with font red, bold black border outline, aligned center. Copy this and paste to L17286 and then also to Q17286:R17286. Do Paste Special Format of the current cell to cells M5:N5, G6:G7, E6:E7, and C6:D6.
 Separate each two adjacent columns of data from the next two by a bold border right outline. Separate all column Headings into their own bold outline boxes. Select cell range A17285:R17285, copy it and paste it to A17287 as backup formulas. There will be temporary errors  those are acceptable. They may have to do with column definitions.
 Select cell K17291 and enter "=MIN(K6:K17285)"; select cell K17292 and enter "=MAX(K6:K17285)". Copy K17291:K17292 to L17291 and Q17291:R17291 as an aid to charting.
Part 2 Explanatory Charts, Diagrams, Photos
 (dependent upon the tutorial data above)
 1Create the chart
 Edit Go To cell range K6:L17286 and using the Chart Wizard or Chart Ribbon select Charts All/Other, Scatter, Smooth Line Scatter. Under Chart Wizard, a new Chart sheet will be created but per the Ribbon, a graph will land atop the data of the Data01 worksheet. Copy (or Cut) this graph and paste it to the top left corner of the Chart worksheet. Hover over the lower right corner until the cursor becomes a doubleheaded arrow and then select the corner and pull the graph into an approximate square. These steps may take some minutes, depending upon your processor. Wait times of 4 minutes were common for such job as a recalculation of new random arrangement, copy picture, etc. Again, it is much faster to have a minichart of columns Q and R with red line, weight 1, on the DATA01 worksheet than to wait the 5 minutes for the actual chart to generate.
 Click in the Plot Area to add series 2. Do menu item Chart Add Data and in response to the range query, activate the Data01 worksheet and Edit Go To cell range Q6:R17285, then click OK. This often comes out wrong and has to be corrected in the formula bar. The two series you want are =SERIES(,'DATA 01'!$K$6:$K$17286,'DATA 01'!$L$6:$L$17286,1) and =SERIES(,'DATA 01'!$Q$6:$Q$17286,'DATA 01'!$R$6:$R$17286,2), in that order (per the last number in the last chart parameter of the foregoing chart function statements). The standard preference is for no grid lines or axes or legend, all of which can be set to none via Chart Layout.
 Under Chart Layout, per clicking in the Plot Area, one reaches at the far left Current Selection  Plot Area  and Format Selection. Under this, the Fill has been set to the Texture Oak, Line has been set to None and no other effects were added.
 Next, the Current Selection is set to Series 1, the bowl, and Format Selection shows that Shadow has been set to Outer, 270 degrees, black, size 100%, blur 4 pt, distance 21 pt and transparency 2%. No glow or soft edges were used. Line = 180 pt weight, style solid dashed, and the gradient picture is presented here (with the final right hand white coming in at 68% and the maroon at 66%):
 Next, the Current Selection is set to Series 2, the cherries, and Format Selection shows that Shadow was set but never turned out, even though none of the cherry's colors are transparent, so for whatever reason. Here is the picture of the Line Gradient for the Cherries, plus some of the colors:
 Starting at 4% White, we then go to Pink/Fuchsia, and so on:

Save the Data chit section from A1:R15 as Formulas, then below that as Paste Special Values to the Saves Worksheet, and under these two sets of data, save a copied picture of the chart by using the shift key + copy and the shift key + paste.  Save the workbook.
Part 3 Helpful Guidance
 1Make use of helper articles when proceeding through this tutorial:
 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.
 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.
Tips


 Here are some other pictures made along the way:








 Clustered stems via adding IF STATEMENT to columns Q and R: "=IF(D6=1,0,(Shrinker2^2*(Stretch_x2*(((BEE^2CEE^2*COS(AYE2_*E6)*COS(AYE2_*E6))^0.5*COS(E6)))+Adj_x2)*FactorUpX))" edited in Q6 and edit filled down to Q17285, then copied to Q17287. Statement formula "=IF(D6=1,0.125,(Shrinker2^2*(Stretch_y2*(((BEE^2CEE^2*COS(AYE2_*E6)*COS(AYE2_*E6))^0.5*SIN(E6))+z2_)+Adj_y2)*FactorUpY))" edited in R6 and filled down to R17285, then copied to R17287. Result:
 After setting spcl 3 unit blocks of averages in columns S  V to collect 3 unit cherries at a time (the stems together), which did not quite work as planned … still, a good result:
 Here are some other pictures made along the way:

 The following section, down to "PostRevision", is "PreRevision" and should be regarded as such, please.


 The above graphic was made by altering the formulas in Q and R to "=IF(D8=1,Avg01x,(Shrinker2^2*(Stretch_x2*(((BEE^2CEE^2*COS(AYE2_*E8)*COS(AYE2_*E8))^0.5*COS(E8)))+Adj_x2)*FactorUpX))" for Q and "=IF(D8=1,Avg01y,(Shrinker2^2*(Stretch_y2*(((BEE^2CEE^2*COS(AYE2_*E8)*COS(AYE2_*E8))^0.5*SIN(E8))+z2_)+Adj_y2)*FactorUpY))" for R for range Q8:R2887. Then Avg02x and Avg02y are used down to 5767, then Avg03x and Avg03y are used down to 8647, then Avg04x and Avg04y are used down to 11527, then Avg05x and Avg05y are used down to 14407, then Avg06c and Avg06y are used down to 16327, and finally Avg07x and Avg07y are used down to 17285  each one being an increment of 3*960 + 7, where column D has 1;s appear if SWS2_ has 18 spheres. In column S from S8:S17285 is the formula "=IF(D8=1,(Shrinker2^2*(Stretch_x2*(((BEE^2CEE^2*COS(AYE2_*E8)*COS(AYE2_*E8))^0.5*COS(E8))) +Adj_x2)*FactorUpX),"")" and similarly in column T is the formula "=IF(D8=1,(Shrinker2^2*(Stretch_y2*(((BEE^2CEE^2*COS(AYE2_*E8)*COS(AYE2_*E8))^0.5*SIN(E8))+z2_)+Adj_y2)*FactorUpY),"")", w/o external quotes. This is Format Filled yellow. In cell U2886 is Avg01x and in V2886 is Avg01y. Beneath those in cell U2887 is the formula "=AVERAGE(S8:S2887)" and in V2887 is "=AVERAGE(T8:T2887)". So these are the Defined Name Variables mentioned in the new formulas in columns Q and R. They take an average of the cherry stem values, when column D=1, in columns S and T (3 values are averaged, for example, tho not necessarily so, depending on the number of cherries or spheres selected by the user). These values then become inputs for columns Q snd R.


 So ... the next variable to define is found 2880 rows down at U5767. Thus at U5766 we find Avg02x and at V5766 is Avg02y, with U5767 having the formula "=AVERAGE(S2888:S5767)" and V5767 "=AVERAGE(T2888:T5767)".
 So then it is a simple matter of copying these and revising the titles of the variables and doing Insert Name Create Name in Top Row, OK, on down until the final formulas in U and V17285 which must be done manually.
 Also, the Q and R formulas need to be edited with the new local (bottom) variable names and Edit Filled Down in correct blocks of 2880 cells to match the Averaging formulas, manually. Then you're done. It's helpful to keep a series of 2880+7 +2880 step value across the top of S to X.
 Lastly, in a search to save time, AYE was set to 1000 and the Line Weight was changed, No time was saved but some weird special effects were created,
 AYE=1000, Line Weight=150
 AYE=1000, Line Weight=80
 AYE=1000, Line Weight=180
 POSTREVISION: New Additional Data Section



 There is still an extra line/stem that is not accounted for by "cherrytwinning" of the randomizing being the same or similar number, but it's very close to a good effect. Still, if the stems were more curved, it would be an improvement.
 The only way found so far to get some stem curvature some of the time is to add a randomizer to the averages. So, for example, in cell U17286 is now the formula "=RANDBETWEEN(5,5)*0.01" and in cell U17285 is the modification "=AVERAGE(S16328:S17285)+U17286". For y, in V17286 is the formula "=RANDBETWEEN(3,9)*0.01" and in cell U18285 is the modification "=AVERAGE(T16328:T17285)+V17286". These same randomizers and modifications were made to each of the 6 other averages. It might help to do a copy and paste special values to give Excel more of a chance to do curve smoothing. It is known that high static y adjustments will lead to curves but that the stems look too long, like a pile of parabolas, which is hardly the natural effect sought either.

 REVISON 2: I now have curving stems via changing the formulas in Q and R respectively to "=IF(D8=1,VLOOKUP(W8,D_Looker,2),IF(S8="B",Q7+COS(Q7*PI()/180)/18,(Shrinker2^2*(Stretch_x2*(((BEE^2CEE^2*COS(AYE2_*E8)*COS(AYE2_*E8))^0.5*COS(E8)))+Adj_x2)*FactorUpX)))" for Q8:Q17285 and "=IF(D8=1,VLOOKUP(W8,D_Looker,3),IF(T8="B",R7+SIN(R7*PI()/180)/18,(Shrinker2^2*(Stretch_y2*(((BEE^2CEE^2*COS(AYE2_*E8)*COS(AYE2_*E8))^0.5*SIN(E8))+z2_)+Adj_y2)*FactorUpY)))" for R8:R17285. Including row 8 in the chart may be a mistake  see for yourself.
 First 985 rows with SWS2_ cherries = 18:
 Q8:R17285 for 18 SWS2_ cherries in a 15 sphere bowl:
 You'll notice the new chart with automatic updating figures on the left (the Randy formulas and Q x formula at bottom are not autoupdating). There are two kinds of formulas for this: 1) For "AYE", the formula in the Text Box is "='DATA 01'!$G$1", w/o external quotes. 2) For AYE's corresponding value of 20, the formula is "='abc (version 1).xlsx'!AYE" where 'abc (version 1).xlsx' is my actual filename  I have also seen xlsb  try that if xlsx won't work (but I can't find any of those now looking through them all). I suggest working with 1 cherry while working with the text boxes to minimize processing time, even if you're on manual calculation. Text boxes are available under Chart Layout  Chart Title  Chart Title Options, where under Text Box, you should check 'Resize shape to fit text' under Autofit. To share a secret though  the text boxes within my chart came from Excel 97 and were adapted, so perhaps you can get a friend to send you some charts full of them because they don't seem to handle too well under Excel 2010/11. For example, the text within them does not show up in the formula bar and is hard to edit.
Warnings
 Processor Time: This workbook chews up processor time. The steps involving the chart may take some minutes, depending upon your processor. Wait times of 4 minutes were common for such job as a recalculation of new random arrangement, copy picture, etc.
 ERRORS: If there are unplanned errors or error values, either the sheet in incomplete and needs further input or Lookup Tables for critical variables or perhaps there's a mistake somewhere along the line. If the instructions have been completed and there are still errors, select the cell that has the error value that is furthest left and topmost first. Look for a typo in a formula or unmatched parentheses. Possibly, a Defined Name is wrong  they need to be input into the formulas exactly as they were defined. Do Insert Name Define to check. If there is a #DIV/0! error, the example does not, so look for a variable that somehow did not get filled in with a value perhaps. At any rate, what to do is select the cell with the error, and after checking all those typical errors, do Tools Auditing Trace Precedents and/or Trace Error. If fixing all the topmost leftmost errors does not fix the rest of your errors on the worksheet, one may need to do it the hard way, from the bottom right upwards then leftwards; that is the slow but sure way to fix all errors.
 Also, errors in the chart data will most likely plot as zeros. This may be acceptable or desirable even. However, if too many lines (or curves) are returning to 0, it may indicate a logical flaw in the data  or too many tiny values and then perhaps rescaling the chart is needed by inspecting the horizontal and vertical axes and changing them to zero in on the problem. Hover over or click on a data marker on the series plot and then do a search in the proper column by value for that value, and identify its precedents.
Sources and Citations
 The Garthwaite Curve shown was first created by Chris Garthwaite in May of 1994 and is based upon the Spherical Helix found on page 264 along with the Sine Wave Sphere on page 266 of "CRC Standard Curves and Surfaces" by David von Seggern, CRC, ANN ARBOR, 1993. ISBN 0849301963
 The workbooks used for this article were " THE Garthwaite Curve"(with spaces)," SineWave On Sphere p 266" (with spaces), "Acquire a Ring of Sinewave Spheres In Excel.xlsx", "Chaos Sinewave On Sphere NO X.xlsx" and "Cherries Chaos SW On Sphere NO X.xlsx"
Article Info
Categories: Graphics  Microsoft Excel Imagery