In this article, you'll learn to make the "uniform spiral" pattern and image below, and the dozens of variations the file permits therefrom.
Steps
Part 1
Part 1 of 4:
Previous Lessons Learned
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1Be sure that you have done the three previous spreadsheets. They are:
- Create Artistic Patterns in Microsoft Excel
- Create a Flower Pattern in Microsoft Excel
- Create a Tornado Screw Pattern in Microsoft Excel
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Complete those first before attempting this one because there was a sequence to building the worksheets.Advertisement
Part 2
Part 2 of 4:
The Tutorial
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Start a new workbook by saving the old workbook under a new name. Save the workbook into a logical file folder.
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Set variables to various values and set formulas correctly.
- Set A4, On=0,Off=1, to 0.
- Set B2, TURNS, to 12.
- Set C1, S's Count, to 144.
- Set D5, AAA, to 0.
- Set E3, Divisor to 160.
- Set H1 to .98 and J1 to .96
- Set E4, YN, to Y.
- The formula in Factor is "=IF(E4="Y",IF(ODD(S_COUNT)=S_COUNT,-S_COUNT*0.01,S_COUNT*0.01),-0.25)"
- Adjuster is set to 1 and AdjRows to 1439.
- t is -308100.
- Adj is "=IF(TURNS>0,VLOOKUP(TURNS,TURNS_LOOKUP,2),VLOOKUP(TURNS, TURNS_LOOKUP_NEG,2))"
- Designer is "=VLOOKUP(S_COUNT,SPHEROIDS_COUNT_LOOKER,2)"
- Var is "=IF(S_COUNT<4,S_COUNT+30,12)"
- Cc is "=-0.25*PI()/C3"
- db is 4.5
- top is "=ROUND((-B4*PI())+(Adj),0)" 968,277
- H2 is Sync1 "=H1/GMLL"
- J2 is Sync2 "=J1/GMSL"
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None of the Lookup tables have changed.
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The column formulas are as follows:
- B7: "=IF(EVEN(S_COUNT)=S_COUNT,ROUND((-B4*PI())+(Adj),0),top)"
- B8;B1447: "=((B7+(-TOP*2)/(AdjRows)))*$B$1"
- C7: "=ROUND(-EXP((PI()^2)+(Cc*-(db))),0)+Designer"
- C8:C1447: "=C7"
- D7:D1447: "=IF(A7=0,D6,DEGREES((ROW()-7))*COS((ROW()-7)*Factor*PI()/(180))/Divisor)" which looks new.
- E7:E1447: "=IF(A7=0,E6,DEGREES((ROW()-7))*SIN((ROW()-7)*Factor*PI()/(180))/Divisor)"
- F7:F1447: "=IF(A7=0,F6,((PI())*((SIN(B7/(C7*2))*GMLL*COS(B7)*GMLL*(COS(B7/(C7*2)))*GMLL)+D7)))"
- G7:G1447: "=IF(A7=0,G6,((PI())*((SIN(B7/(C7*2))*GMLL*SIN(B7)*GMLL*(COS(B7/(C7*2)))*GMLL)+E7)))"
- H7:H1447: "=F7*GMLL*Sync1"
- I7:I1447: "=G7*GMLL*Sync1"
- J7:J1447: "=F7*GMSL*Sync2"
- K7:K1447: "=G7*GMSL*Sync2"
- A7:A1447: (without spaces) "=IF(OR(AND((ROW()-7)>Rrs,(ROW()-7)<=Rrs*2),AND((ROW()-7)>Rrs*4,(ROW()-7)<=Rrs*5), AND((ROW()-7)>Rrs*7,(ROW()-7)<=Rrs*8), AND((ROW()-7)>Rrs*10,(ROW()-7<=Rrs*11),AND((ROW()-7)>Rrs*13,(ROW()-7<=Rrs*14), AND((ROW()-7)>Rrs*16,(ROW()-7<=Rrs*17), AND((ROW()-7)>Rrs*19,(ROW()-7)<=Rrs*20), AND((ROW()-7)>Rrs*22,(ROW()-7<=Rrs*23), AND((ROW()-7)>Rrs*25,(ROW()-7)<=Rrs*26), AND((ROW()-7)>Rrs*28,(ROW()-7)<=Rrs*29), AND((ROW()-7)>Rrs*31,(ROW()-7)<=Rrs*32), AND((ROW()-7)>Rrs*34,(ROW()-7)<=Rrs*35), AND((ROW()-7)>Rrs*37,(ROW()-7)<=Rrs*38), AND((ROW()-7)>Rrs*40,(ROW()-7)<=Rrs*41)),0,1)+On_0_Off_1
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Part 3
Part 3 of 4:
Explanatory Charts, Diagrams, Photos
- (dependent upon the tutorial data above)
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Create the charts. These flow from F7:G1446, H7:I1446 and J7:K1446, the latter two being copied in or Added Series independently and corrections made until the series look like this:
- =SERIES(,'CosSin to Base X,Y DATA'!$H$7:$H$1446,'CosSin to Base X,Y DATA'!$I$7:$I$1446,1) in ice blue or green-blue, it's hard to tell. Line weight is .25 for all.
- =SERIES(,'CosSin to Base X,Y DATA'!$J$7:$J$1446,'CosSin to Base X,Y DATA'!$K$7:$K$1446,2) in red-lavender
- =SERIES(,'CosSin to Base X,Y DATA'!$F$7:$F$1446,'CosSin to Base X,Y DATA'!$G$7:$G$1446,3) in blue
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Remove Axis, Grid lines and Chart Legend for both charts in Chart Layout.Advertisement
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Tips
- 144/6 spiral arms = 24, so 24 * 13 = 312. Inputting 312 into S's Count gives the following rendering:Thanks
- Many other designs are possible -- here's one:Thanks
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Warnings
- ERRORS: If there are errors or error values, either the sheet in incomplete and needs further input or Lookup Tables for critical variables or perhaps there is 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's #DIV/0!, the example does not, so look for a variable that somehow did not get filled in with a value perhaps. At any rate, 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 the 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.Thanks
- Also, errors in the 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.Thanks
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References
- The source file used for this article was "Garthwaite LINE07.xlsx"
About this article
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