Create a Spiral That Pauses As a Circle

Nuclear scientists will tell you that an electron takes "no path" between up to 8 orbital shells. A few years ago, the following design was discovered which might cause one to wonder if they're correct, for it shows orbits with spirals in between. Learn to make these in the following steps.

Steps

The Tutorial

  1. Open a new workbook in Excel and create 3 worksheets: Data, Chart and Saves. Save the workbook into a logical file folder.
  2. Set Preferences. Open Preferences in the Excel menu. 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, Limit iteration checked, max iterations 100, max change .000,000,000,000,01 w/o commas as this problem involves precise goal seeking and save external link values and use 1904 date 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. Although it will be shown HOW it works, it will not be explained WHY it works, and as such should be considered proprietary, though you are free to figure it out if you can.
  4. Enter Defined Variable names in row 1: B1: PiTop; C1: N; E1: p; F1: Factor.
  5. Enter variable values in row 2 and create names: B2: 60; C2: 2; E2: 2; F2: -.25 H2: Charting and I2: Charting. Select B1: F2 and Insert Names Create names in Top Row, OK.
  6. Enter the column headings. A3: a, aA; B3: t, tT; C3: I, iI, D3: cC; E3: zZ; F3: cos; G3: sin; H3: x; I3: y
  7. Select the entire worksheet by selecting between the 1 and A in the top left corner and Format Cells Number Number Decimal Places 4, Alignment Horizontal Center.
  8. Select rows 1:3 and Format Cells Font Red. Format CELLS B2, C2, E2 and F2 Fill Yellow and Border Black bold Outline + Center.
  9. Fill in the columnar data and formulas:
    • Select cell A4 and enter .3, then Edit Go To cell range A5:A725 and enter "=A4" and Edit Fill Down. Insert Name Define Name a to cell $A$4 and Insert Name Define Name aA to cell range $A$4:$A$725.
    • Select cell B4 and enter 0. Insert Name Define name t to cell $B$4.
    • Select cell range B5:B725 and enter w/o quotes the formula into the active cell B5, "=(B4+(PI()*(PiTop-t)/720))". Select cell range B4:B725 and Insert Name Define name tT to cell range $B$4:$B$725.
    • Select cell C4 and enter 1. Insert Name Define name I to cell $C$4.
    • Select cell range C5:C725 and enter w/o quotes the formula into the active cell C5, "=(C4+((N-I)/720))". Select cell range C4:C725 and Insert Name Define name iI to cell range $C$4:$C$725.
    • Select cell D4 and enter 3. Insert Name Define name cC to cell range $D$4:$D$725. Edit Go To cell range D5:D725 and with D5 active, enter the formula w/o quotes "=D4" and Edit Fill Down.
    • Select cell range A4:D4 and Format Cells Fill Yellow to designate them as input cells.
    • Edit Go To cell range E4:E725 and Insert Define Name zZ to cell range $E$4:$E$725, then enter into E4 the active cell the formula w/o quotes "=tT/(p*cC)" and Edit Fill Down.
    • Edit Go To cell range F4:F725 and with F4 active, enter w/o quotes the formula "=COS((ROW()-4)*Factor)" and Edit Fill Down.
    • Edit Go To cell range G4:G725 and with G4 active, enter w/o quotes the formula "=SIN((ROW()-4)*Factor)" and Edit Fill Down.
    • Edit Go To range H4:H725 and with H4 active, enter w/o quotes the formula "=(aA*COS(-tT-(2*PI()*iI)/N)*zZ)+F4" and Edit Fill Down.
    • Edit Go To range I4:I725 and with I4 active, enter w/o quotes the formula "=(aA*SIN(-tT-(2*PI()*iI)/N)*zZ)+G4" and Edit Fill Down.

Explanatory Charts, Diagrams, Photos

  • (dependent upon the tutorial data above)
  1. Create the Chart shown at the beginning of the article.
    • Edit Go To cell range H4:I725 and, using either the Chart Wizard or the Ribbon, select Charts, All/Other, scroll down to Scatter, Smoothed Line Scattered and select it. A small chart will either appear in a new window (Chart Wizard) or near your data (Ribbon users). For the latter, Copy or Cut the chart and activate the Chart worksheet and paste it into cell A16. Using the cursor to hover over the lower left hand corner of the chart until it becomes a double-headed arrow, pull the chart down and to the right to form a larger square at about K66. Double-click on the series plot line and change line Weight to 1. Activate the Data sheet and copy cell range A1:I14 and activate the Chart worksheet and paste the formulas atop the chart. In cell A1 note "To row 725". Do a Copy Picture and Paste Picture to the Saves worksheet with the shift key held down throughout. Save the workbook.
  2. To make 8 orbital shells, change variable PiTop in cell B2 to 145 and change Factor in cell F2 to 12. Here is the chart resulting from those two changes:

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 Microsoft Excel Imagery, Mathematics, Spreadsheets or 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

  • Many other designs are possible using this data configuration. Here are a few:
    • PiTop 6, Factor -.5, a=2, I = 10
    • PiTop 55, Factor -.25, p 2, n 2, a .3 I 1 Tao Spiral
    • PiTop 57
    • PiTop 64 Factor 18 p 2 n 2 a .3 t 0 I 1 cC 3
    • Try PiTop=38, n=2, p=2, Factor=18, a=.3, t=0, I=2, cC=3
    • Cursive -- PiTop=blank, n=2, p=2, Factor=.014, a=.3, t=0, I=1, cC=3

Warnings

  • ERRORS: If you have errors or error values, either the sheet in incomplete and needs further input or Lookup Tables for critical variables or perhaps you've made 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 you have DIV/0!, I do not, so look for a variable that somehow did not get filled in with a value perhaps. At any rate, what you want 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 your worksheet, you 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 your chart data will most likely plot as zeroes. 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.

Related Articles

Sources and Citations

  • The file used to create this article was "SPIRAL PAUSES AS CIRCLE.xlsx"
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