# How to Create a Chaos Ring of Sinewave Spheres

Three Parts:The TutorialExplanatory Charts, Diagrams, PhotosHelpful Guidance

Follow this article to learn how to create a Chaos Ring of Sinewave Spheres in Microsoft Excel and to make this image and many more like it, but different.

### Part 1 The Tutorial

- 1
**Open a new Excel workbook and create 3 worksheets (except Chart if you are using Chart Wizard).**Name them Data, Chart and Saves. If you have completed the Article and workbook How to Acquire a Ring of Sinewave Spheres, we'll be using that article for our model and quite a bit of time can be saved by looking for**MODIFIED**or**NEW**sections after doing a SAVE AS of the first workbook under a name appropriate to the present project. The workbook being used for this article is titled*Chaos Sinewave On Sphere NO X.xlsx*Otherwise, simply follow the steps in order. #* As a warning note that this process uses the RandBetween function with over 34,0000 cells involved and can take large amounts of processing time. Please set the Calculation setting to Manual and carefully follow the instructions to PASTE VALUES as given. - 2
**Set 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*and*calculate before save*are checked. Set max change to .000,000,000,000,01 without commas as goal-seeking is 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*.

- In General, set
- 3
**It helps by placing the cursor at cell A16 and doing Freeze Panes.**Edit Go To cell range A1:N17288 and Format Cells Number Number Decimal Places 4, Font Size 9 or 10, Fill (from the color wheel) a nice fuchsia and make the Border Dark Blue bold Outline. - 4
**Enter the upper Defined Name Variables Section (here's a picture):**- Cell A1: Enter Sinewave Spheres in a Chaos Ring
- B2: Enter Pasted and C2: Enter Values. Format Fill Red and Font White.
- E1: AYE
- E2: BEE
- E3: CEE
- F1: 10
- F2: .50
- F3: .50
- Select cell range E1:F3 and Insert Name Create Names in Left Column, OK.
- G1: Stretch_y1
- H1: Stretch_x1
- G3: Shrinker
- H3: Enter "=0.1*12/SPHERES" and Insert Name Define Name Shrinker to cell $H$3.
- I3: SPHERES
- J3: 24
- I1: ROWS
- I2: MAGIC
- Select cell range I1:J3 and Insert Name Create Names in Left Column, OK.
- J1: Enter "=17285-5"
- J2: Enter "=ROWS/SPHERES"
- G2: Enter "=(8.5*(SHRINKER*10))"
- H2: Enter "=(8.5*(SHRINKER*10))"
- Select cell range G1:H2 and Insert Name Create Names in Top Rows, OK.

- 5
**MODIFIED:**Enter the column heading of rows 4 and 5:- A5: Adj Cos (for Adjusted Cosine)
- B5: Adj Sin
- C5: Indicator
- NEW: D4: Enter .=RANDBETWEEN(4,7)/100 where if the period is deleted the formula becomes active.
- D5: Randy (for RandBetween)
- E5: t: 0 to nπ
- F5: z1_
- G5: Adj_x1
- H5: Adj_y1
- I4 and J4: Charting
- I5: x: No z
- J5: y: With z
- NEW: K5: Adj_x2 (not used but conceivably could be in future; if so the formula would be "=IF(C6=1,D6,K5)"
- NEW: L5: Adj_y2
- NEW: M4 and N4: Charting
- NEW: M5: x2: No Z (not used but conceivably could be in future; if so the formula would be "=SHRINKER^2*(Stretch_y1*(((BEE^2-CEE^2*COS(AYE*E6)*COS(AYE*E6))^0.5* SIN(E6))+z1_)+Adj_x1*0.5)+Adj_x2"
- NEW: N5: y2: With z.
- Command+Select cells F1:F3 and I3 and Format Fill yellow.
- Select cell J3 and Format Fill sky blue from the color wheel.
- Select cell range I4:J5 and Format Font italic.
- NEW: Select cell range M4:N5 and Format Font italic.
- NEW: Command+Select cells A1:D1, A2, A3:D3, D2, G1:N2, G3:H3, M3:N3 and Format Fill White.

- 6
**Enter the column formulas - BE VERY CAREFUL TO COPY AND PASTE VALUES as specified please.**- Adj Cos: Edit Go To cell range A6:A17285 and enter into A6 w/o quotes the following formula, "=17*COS((ROW()-6)*0.25/12*PI()/180)" and Edit Fill Down. The .25 is for 1440*.25 = 360. 17280/12=1440. So we are taking 1/12th of 1/4 or 1/48th of 17280 = 360, the degrees of the trig function cosine for a circle. PI()/180 converts radians to degrees. (ROW()-6) in row 6 = 0, so we start off taking the cosine of 0, which is 1, and multiplying it by 17. 17 is twice the Stretch factor, and if I recall rightly, is 1/2 the radius of the ring (the Stretch factor operates from each sphere's center). However, Shrinker is also involved, as you'll see later.
- Adj Sin: Edit Go To cell range B6:B17285 and enter into B6 w/o quotes the following formula,"=17*SIN((ROW()-6)*0.25/12*PI()/180)+17"and Edit Fill Down, which is different than the above one for cosine by the addition of 17 to it. All in all, that give us 4*8.5, and that is the radius, as I recall.
- Indicator: Select cell C6 and enter 1. Edit Go To cell range C7:C17286 and enter w/o quote the formula, "=IF((ROW()-7)/MAGIC=INT((ROW()-7)/MAGIC),1,IF((ROW()-7)=0,1,0))" and Edit Fill Down. This formula says, 'Take a look at the row I'm in, divide it by the number of rows per sphere (MAGIC) and if that number is an integer, return a 1, otherwise if I'm in the next-to-top row also return a 1, otherwise, return a 0.' So now there is an indicator of where 1 sphere ends and the next one begins, no matter how many spheres the user selects to chart.
- MODIFIED: Randy: Edit Go To cell range D6:D17286 and enter into D6 w/o quotes the following formula,"=RANDBETWEEN(4,7)/100" and Edit Fill Down. Warning: Make calculation Manual before adding this variable or column into your formulas, especially as a factor, as it can take 20 minutes to calculate and draw the new chart. It is not currently employed, but a copy of its formula has been saved at the bottom of the x and y formulas. Edit Go To cell range D6:D17285 and Insert Name Define Name Randy to cell range $D$6:$D$17285. Also, Edit Go To cell range D6:D17286 and Copy, then Paste Values right back to cell D6:D17286.
- t: 0 to nπ: Select cell E6 and enter 0. Select cell E7 and enter the formula "=(2*PI()/MAGIC)". Edit Go To cell range E8:E17285 and enter w/o quotes into E8 the formula "=IF(C8=1,2*PI(),2*PI()/MAGIC+E7)" and Edit Fill Down.
- z1_: Edit Go To cell range F6:F17285 and enter w/o quotes into F6 the formula "=CEE*COS(AYE*E6)" and Edit Fill Down. Edit Go To cell range F6:F17285 and Insert Name Define Name z1_ to cell range $F$6:$F$17285.
- Adj_x1: Edit Go To cell range G6:G17285 and enter w/o quotes into G6 the formula "=IF(C6=1,A6,G5)" and Edit Fill Down. Edit Go To cell range G6:G17285 and Insert Name Define Name Adj_x1 to cell range $G$6:$G$17285. This makes a constant adjustment as if one were referencing a new center of every new sphere from Adj Cos, else it takes the value just above itself.
- Adj_y1: Edit Go To cell range H6:H17285 and enter w/o quotes into H6 the formula "=IF(C6=1,B6,H5)" and Edit Fill Down. Edit Go To cell range H6:H17285 and Insert Name Define Name Adj_y1 to cell range $H$6:$H$17285. This makes a constant adjustment as if one were referencing a new center of every new sphere from Adj Sin, else it takes the value just above itself.
- x: No z: Edit Go To cell range I6:I17285 and enter w/o quotes into I6 the formula "=SHRINKER^2*(Stretch_x1*(((BEE^2-CEE^2*COS(AYE*E6)*COS(AYE*E6))^0.5 *COS(E6)))+Adj_x1)" and Edit Fill Down. This is the x part of the heart of the sinewave sphere formula from the text, without the z dimension added or multiplied in, which is why it took me so long to discover how to make it work.
- y: With z: Edit Go To cell range J6:J17285 and enter w/o quotes into J6 the formula "=SHRINKER^2*(Stretch_y1*(((BEE^2-CEE^2*COS(AYE*E6)*COS(AYE*E6))^0.5* SIN(E6))+z1_)+Adj_y1)" and Edit Fill Down. This is the y part of the heart of the sinewave sphere formula from the text, with the z dimension added in, which is why it took me so long to discover how to make it work. In the spirallic spheroids Garthwaite Curve, the z-dimension is multiplied into both x and y parts. Furthermore, there was no adjustment for the GOLDEN MEAN Long Leg, which was expected all along, until it worked without it. The other curve doesn't.
- Select cell I17286 and enter the formula w/o quotes "=I6" and select cell J17286 and enter the formula w/o quotes "=J6". This makes the top connecting line from the last sphere to the first.
- Edit Go To cell range I6:J17288 and do Format Fill sky blue. Edit Go To cell range M6:N17288 and Format Fill sky blue.
- Select cell D5 and Format Fill light sea green, font red, Border navy blue outline bold. Copy this cell to H17287. Then do Edit Paste Special Format of this cell to cell C6, E6, E7, I17286, J17286, M17286 and N17286 to make distinct the format of those cell's formulas/values.
- NEW: COPY CELL RANGE A11:J17285 and then PASTE SPECIAL VALUES right back atop the same cell range. Format Fill Red and Font White. This means that the top Variables section is no longer operative in any useful way until you Edit Fill Down the formulas from row 10, which may mean having to wait a considerable length of time, as in 25 - 40 minutes. It can also take that long to save the workbook, so ...
- NEW: Save the workbook.
- NEW: Adj_y2: Edit Go To cell range L6:L17285 and enter w/o quotes into L6 the formula "=IF(C6=1,Randy,L5)" and Edit Fill Down. COPY CELL RANGE L11:L17285 and then PASTE SPECIAL VALUES right back atop the same cell range. Format Fill Red and Font White.
- NEW: y2: With z: Edit Go To cell range M6:M17285 and enter w/o quotes into M6 the formula "=SHRINKER^2*(Stretch_y1*(((BEE^2-CEE^2*COS(AYE*E6)*COS(AYE*E6))^0.5* SIN(E6))+z1_)+Adj_y1*0.5)+Adj_y2" and Edit Fill Down. COPY CELL RANGE M11:M17285 and then PASTE SPECIAL VALUES right back atop the same cell range. Format Fill Red and Font White.
- Select cell N17286 and enter "=N6", w/o quotes.
- Hopefully, that avoided all the waiting and waiting for processing time to pass. We'll see.

### Part 2 Explanatory Charts, Diagrams, Photos

- (dependent upon the tutorial data above)

- 1
**Create the chart.**- Edit Go To cell range I6:J17286 and from the Ribbon or Chart Wizard select Charts All/Other Scatter Smoothed Line Scatter and Copy or Cut the chart that is atop the data worksheet and paste it to the top left of the Chart worksheet. Hover over the lower right corner until the cursor becomes a double-headed arrow and pull it open to become a large approximate square.
- Click in the Plot Area and select Chart Layout from the ribbon and at far left under Current Selection select Series 1, then under that, Format Selection. Set Line to Kelly Green, Smoothed line, Transparency 27%, Weight = 1 pt. and Dashed = Heavy Dashed Dots. Set Shadow to checked Outer 315 degrees, black, Size 100%, Blur 4 pt, Distance 54 pt, Transparency 2 %. Set Glow to fire engine red Size = 4 pt. 74% transparency, Soft Edges 0 pt. Then click on OK.
- Do Current Selection under Chart Layout as Plot Area, Format Selection. No Line, No Glow and No Shadow. Set Fill to Gradient to Aubergine left 0% and Foresty Blue Green at 70%; Radial Centered and Rotate gradient with shape check-box in lower left checked. Then click on OK.
- Do menuitem Chart Add Data and respond to the range query by selecting M6:N17286 on the Data worksheet. This you will want to edit in the Chart worksheet formula bar until it becomes "=SERIES(,'DATA 01'!$I$6:$I$17286,'DATA 01'!$N$6:$N$17286,2)", w/o quotes.
- Click in the Plot Area and select Chart Layout from the ribbon and at far left under Current Selection select Series 2 (or 3, whatever), then under that, Format Selection. Set Line to Bright Sky Blue, Smoothed line, Transparency 0%, Weight = 2 pt. (see TIPS below -- the example above is 3.75 tho) and Style Dashed is Solid. Set Shadow to checked Outer 315 degrees, black, Size 100%, Blur 4 pt, Distance 96 pt, Transparency 57 %. Set Glow to fire engine red Size = 4 pt. 50% transparency, Soft Edges 0 pt. OK - done √

### Part 3 Helpful Guidance

- 1
**Make 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

## Warnings

- 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 0-8493-0196-3
- 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" and mostly "Chaos Sinewave On Sphere NO X.xlsx"
- See MyCurve.org

## Article Info

Categories: Microsoft Excel Imagery | Graphics