How to Create Bifurcation Theory Catastrophe Curves in XL

Step-by-Step Guide

1. 1

   Step 1: Start by opening a new workbook in Excel from the desktop

   Double click on Excel (either the green X on the dock or the app title in the folder) and select File New Workbook. ,, Doing so will select the entire worksheet.
   
   Format Cells Number Number to decimal places 2, show comma.
   
   Format Cells Alignment Center.
   
   Title the first worksheet, "Elliptic umbilic catastrophe".,,,, A chart will appear atop your data which you should move to the right, beside the data.
   
   Click inside the chart and Do Chart Layout and do Chart Title.
   
   Title it "Elliptic Umbilic Catastophe Curve".
   
   Double click in the Plot Area and format fill sand yellow; double click in the outer chart area and Format Fill orange; click on the data series and then line and do Line Weight 3 pt, Gradient Rust Brown 0%, Dark Purple 74%, Medium Purple 100%.
   
   Your chart should resemble this one: , Title the new worksheet, "Saves"., Type Formulas: into cell A1 and type Values: into cell A11.
   
   Select the "Elliptic umbilic catastrophe" worksheet and select the new chart and with the Shift Key depressed, do Edit Copy Picture, then select the Saves worksheet and to the right or bottom of your data, depress the Shift Key again and do Edit Paste Picture. , Tap on the new worksheet "+" tab button and create a new worksheet; Paste to cell A1 the contents of the clipboard.
   
   Name the new worksheet, "Hyperbolic umbilic catastrophe"
   
   w/o the quotes.
   
   Do Format Column AutoFit Selection
2. 2

   Step 2: from the dock

   ,, A chart will appear atop your data which you should move to the right, beside the data.
   
   Click inside the chart and Do Chart Layout and do Chart Title.
   
   Title it "Hyperbolic Umbilic Catastophe Curve".
   
   Double click in the Plot Area and format fill sky blue; double click in the outer chart area and Format Fill sky blue.
   
   Your chart should resemble this one: , Type Formulas: into cell A24 and type Values: into cell A34.
   
   Select the "Hyperbolic umbilic catastrophe" worksheet and select the new chart and with the Shift Key depressed, do Edit Copy Picture, then select the Saves worksheet and to the right or bottom of your data, depress the Shift Key again and do Edit Paste Picture. , Tap on the new worksheet "+" tab button and create a new worksheet; Paste to cell A1 the contents of the clipboard.
   
   Name the new worksheet, "Parabolic umbilic catastrophe"
   
   w/o the quotes.
   
   At column F, do Insert Column.
   
   Also Insert Column to the right of c*y, and on the right side, to the right of c and c*y again; to the right of each c, enter d, and to the right of each c*y, enter d*y; Do Format Column AutoFit Selection
3. 3

   Step 3: or from within your Applications folder inside the Microsoft folder.

   ,, A chart will appear atop your data which you should move to the right, beside the data.
   
   Click inside the chart and Do Chart Layout and do Chart Title.
   
   Title it "Parabolic Umbilic Catastophe Curve".
   
   Double click in the Plot Area and format fill red; double click in the outer chart area and Format Fill canary yellow.
   
   Your chart should resemble this one: , Type Formulas: into cell A49 and type Values: into cell A54.
   
   Select the "Parabolic umbilic catastrophe" worksheet and select the new chart and with the Shift Key depressed, do Edit Copy Picture, then select the Saves worksheet and to the right or bottom of your data, depress the Shift Key again and do Edit Paste Picture. ,, For example, take the following regarding elementary catastrophes:
   Catastrophe theory analyses degenerate critical points of the potential function — points where not just the first derivative, but one or more higher derivatives of the potential function are also zero.
   
   These are called the germs of the catastrophe geometries.
   
   When the degenerate points are not merely accidental, but are structurally stable, the degenerate points exist as organizing centers for particular geometric structures of lower degeneracy, with critical features in the parameter space around them.
   
   If the potential function depends on two or fewer active variables, and 5 or fewer active parameters, then there are only 11 generic structures for these bifurcation geometries, with corresponding standard forms into which the Taylor series around the catastrophe germs can be transformed., 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.
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   Step 4: In Preferences

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   Step 5: set R1C1 to unchecked or Off

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   Step 6: set Ribbon to checked or On and set Show Formula Bar to checked or On.

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   Step 7: Click in the far upper left top corner above the 1 of row 1 and to the left of column A.

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   Step 8: Enter the Row 1 Column Headers: Enter to cell C1

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   Step 9: 1; Enter to cell D1

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    Step 10: 2; Enter to cell E1

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    Step 11: 3; Enter to cell K1

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    Step 12: Chart: V'X = ShrinkExpand_2*V+X_Offset_D; Enter to cell L1

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    Step 13: Chart: V'Y = ShrinkExpand_1*V+Y_Offset_C; Enter to cell O1

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    Step 14: .5; Enter to cell P1

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    Step 15: -.5; Enter to cell Q1

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    Step 16: .1250; Format Cells O1:Q1 Number Number Decimal Places 4;

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    Step 17: Enter the Row 2 Column Headers: Enter to cell A2

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    Step 18: x; Enter to cell B2

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    Step 19: y; Enter to cell C2

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    Step 20: a; Enter to cell D2

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    Step 21: b; Enter to cell E2

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    Step 22: c; Enter to cell F2

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    Step 23: (x^3)/3; Enter to cell G2

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    Step 24: x*y^2; Enter to cell H2

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    Step 25: a*(x^2+y^2); Enter to cell I2

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    Step 26: b*x; Enter to cell J2

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    Step 27: c*y; Enter to cell K2

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    Step 28: Formula: V=(x^3)/3-xy^2+a*(x^2+y^2)+bx+cy; Enter to cell L2

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    Step 29: Formula: V=(x^3)/3-xy^2+a*(x^2+y^2)+bx+cy; Copy cell range A2:J2 and Paste it to cell range M2:V2; Select cell range A2:K2 and Format Cells Font Bold

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    Step 30: Red; Select cell range L2:V2 and Format Cells Font Bold

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    Step 31: Dark Blue; Enter to cell W2

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    Step 32: ShrinkExpand_1; Enter to cell X2

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    Step 33: .1; Enter to cell W3

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    Step 34: X_Offset_C; Enter to cell X3

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    Step 35: 2; Enter to cell W4

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    Step 36: Y_Offset_C; Enter to cell X4

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    Step 37: 2; Enter to cell W5

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    Step 38: ShrinkExpand_2; Enter to cell X5

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    Step 39: 2; Enter to cell W6

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    Step 40: X_Offset_D; Enter to cell X6

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    Step 41: 6; Enter to cell W7

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    Step 42: Y_Offset_D; Enter to cell X7

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    Step 43: 2 Select cell range W2:X7 and Insert Name Create Names in Left Column

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    Step 44: OK; Format Cells Border Red Boldest Outline; Select Cell Range W2:X4 and Format Cells Border Red Boldest Outline; Select cell range X2:X7 and Format Cells Fill Yellow; (for input changes) Enter to cell Y2

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    Step 45: Y-COMPONENT and Format Cells Font Bold

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    Step 46: Color Dark Blue; Copy cell Y2 to cell range Y3:Y4; Enter to cell Y5

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    Step 47: X-COMPONENT and Format Cells Font Bold

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    Step 48: Color Red; Copy cell Y5 to cell range Y6:Y7; Copy cell X7 to cell X8

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    Step 49: enter 50; Format cell Border Red Boldest Outline

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    Step 50: Font Bold; Enter to cell Y8

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    Step 51: CommonDivisor and select cell range X8:Y8 and Insert Name Create in Right Column

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    Step 52: Enter Columnar Formulas: Enter to cell A3 the formula

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    Step 53: =COS((ROW()-2)*PI()/180); Enter to cell B3 the formula

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    Step 54: =SIN((ROW()-2)*PI()/180); Enter to cell C3 the value

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    Step 55: 1; Enter to cell D3 the value

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    Step 56: 2; Enter to cell E3 the value

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    Step 57: 3; Enter to F3 the formula

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    Step 58: =(A3^3)/3; Enter to G3 the formula

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    Step 59: =A3*B3^2; Enter to H3 the formula

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    Step 60: =C3*(A3^2+B3^2); Enter to I3 the formula

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    Step 61: =D3*A3; Enter to J3 the formula

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    Step 62: =E3*B3; Enter to K3 the formula

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    Step 63: =ShrinkExpand_2*(F3-G3+H3+I3+J3)+X_Offset_D; Enter to L3 the formula

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    Step 64: =ShrinkExpand_1*(R3-S3+T3+U3+V3)+Y_Offset_C; Copy cell range A3:J3 and Paste it to M3:V3; Enter to O3 the value

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    Step 65: .5; Enter to P3 the value

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    Step 66: -.5; Enter to Q3 the value

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    Step 67: .125; Select cell range O3:Q3 and Format Cells Fill Yellow

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    Step 68: Font Red

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    Step 69: Bold; (for input) Select columns A:Y and Do Format Column AutoFit Selection; Copy A3:V3 and Paste it to A4; Enter to cell C4 the formula

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    Step 70: =C3; Enter to cell D4 the formula

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    Step 71: =D3; Enter to cell E4 the formula

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    Step 72: =E3; Enter to cell O4 the formula

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    Step 73: =O3; Enter to cell P4 the formula

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    Step 74: =P3; Enter to cell Q4 the formula

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    Step 75: =Q3; Format Cells O4:Q4 Fill Light Blue; Do menu item Window Split at cell A30; With the cursor in cell A31

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    Step 76: Edit Go To cell A363; Select cell range A363:V4 and Edit Fill Down.

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    Step 77: Select cell range K3:L363 and either Insert Chart or do Chart Wizard or do the Ribbon Charts and Select All

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    Step 78: Scatter

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    Step 79: Smooth Lined Scatter.

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    Step 80: Create a new worksheet by tapping on the "+" tab at the bottom of the worksheets

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    Step 81: to the right.

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    Step 82: Select the "Elliptic umbilic catastrophe" worksheet and select cell range A1:Y8

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    Step 83: and select the new Saves worksheet and Paste the formulas into cell A2

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    Step 84: then select the Elliptic umbilic catastrophe worksheet and select cell range A1:Y8

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    Step 85: and select the new Saves worksheet and Paste the formulas but then do Paste Special Values into cell A12

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    Step 86: which will be a fast way of doing the cell formats too (although there may be a faster way).

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    Step 87: Select the "Elliptic umbilic catastrophe" worksheet and select cell range A1:Y8 and copy it.

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    Step 88: Change Column Headings: Enter to cell F1

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    Step 89: and Format Cells Alignment Center; Copy cell F1 and paste it to cells G1:H1 and cell range R1:T1; Enter to cell F2

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    Step 90: x^3; Enter to cell G2

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    Step 91: y^3; Enter to cell H2

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    Step 92: a*x*y; Enter to cell K2: Formula: V=x^3+y^3+a*x*y+b*x+c*y and copy it and select cell L2 and Paste Special Values; Select cell range F2:H2 and copy it and select cell R2 and Paste Special Values;

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    Step 93: Change the Formulas: Enter to cell F3 the formula

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    Step 94: =(A3^3); Enter to cell G3 the formula

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    Step 95: =(B3^3); Enter to cell H3 the formula

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    Step 96: =C3*A3*B3; Copy cell range F3:G3 and paste to cell range F4:H363; And paste to cell range R3:T363.

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    Step 97: Select cell range K3:L363 and either Insert Chart or do Chart Wizard or do the Ribbon Charts and Select All

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    Step 98: Scatter

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    Step 99: Smooth Lined Scatter.

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     Step 100: Select the "Hyperbolic umbilic catastrophe" worksheet and select cell range A1:Y8

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     Step 101: and select the new Saves worksheet and Paste the formulas into cell A25

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     Step 102: then select the Elliptic umbilic catastrophe worksheet and select cell range A1:Y8

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     Step 103: and select the new Saves worksheet and Paste the formulas but then do Paste Special Values into cell A35

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     Step 104: which will be a fast way of doing the cell formats too (although there may be a faster way).

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     Step 105: Select the "Elliptic umbilic catastrophe" worksheet and select cell range A1:Y8 and copy it.

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     Step 106: Change Column Headings: Enter to cell F1

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     Step 107: and Format Cells Alignment Center; Copy cell F1 and paste it to cells G1:L1 and paste special to cell range T1:Z1; Enter to cell F2

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     Step 108: d; Enter to cell G2

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     Step 109: x^2*y; Enter to cell H2

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     Step 110: y^4; Enter to cell I2

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     Step 111: a*x^2; Enter to cell J2

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     Step 112: b*y^2; Enter to cell K2

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     Step 113: c*x; Enter to cell L2

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     Step 114: d*y; Select cell range F2:L2 and copy it and select cell T2 and Paste Special Values;

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     Step 115: Change the Formulas: Enter to cell F3 the formula

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     Step 116: 4; Enter to cell G3 the formula

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     Step 117: =(A3^2)*B3; Enter to cell H3 the formula

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     Step 118: =B3^4; Enter to cell I3 the formula

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     Step 119: =C3*A3^2; Enter to cell J3 the formula

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     Step 120: =D3*B3^2; Enter to cell K3 the formula

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     Step 121: =E3*A3; Enter to cell L3 the formula

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     Step 122: =F3*B3; Copy cell range A3:L3 and paste to cell range A4:L363; Copy cell range G3:L3 and paste it to U3; Select cell range U3:Z363 and Edit Fill Down; Copy cell range A3:B363 and paste it to O3:P363; Enter to cell Q3

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     Step 123: .5; Enter to cell R3

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     Step 124: -.5; Enter to cell S3

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     Step 125: .125; Enter to cell T3

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     Step 126: -.125; Enter to cell Q4 the formula

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     Step 127: =Q3; Enter to cell R4 the formula

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     Step 128: =R3; Enter to cell S4 the formula

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     Step 129: =S3; Enter to cell T4 the formula

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     Step 130: =T3; Select cell range Q4:T4 and Format Cells Fill sky blue and Select cell range Q4:T363 and Edit Fill Down; Enter to cell M3 the formula

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     Step 131: =ShrinkExpand_2*(G3+H3+I3+J3+K3+L3)+X_Offset_D; Enter to cell N3 the formula

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     Step 132: =ShrinkExpand_1*(U3+V3+W3+X3+Y3+Z3)+Y_Offset_C; Select M3:N363 and Edit Fill Down.

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     Step 133: Select cell range M3:N363 and either Insert Chart or do Chart Wizard or do the Ribbon Charts and Select All

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     Step 134: Scatter

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     Step 135: Smooth Lined Scatter.

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     Step 136: Select the "Parabolic umbilic catastrophe" worksheet and select cell range A1:Y8

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     Step 137: and select the new Saves worksheet and Paste the formulas into cell A50

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     Step 138: then select the Parabolic umbilic catastrophe worksheet and select cell range A1:Y8

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     Step 139: and select the new Saves worksheet and Paste the formulas but then do Paste Special Values into cell A55

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     Step 140: which will be a fast way of doing the cell formats too (although there may be a faster way).

141. 141

     Step 141: Here are the settings and details and other charts you can create with similar / related formulations: Formula: V=(x^3)/3-xy^2+a*(x^2+y^2)+bx+cy; a

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     Step 142: c on left = 1

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     Step 143: 3 and on the right a

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     Step 144: c = .5

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     Step 145: .125; Formula: V=(x)/3-xy+a*(x^2+y^2)+bx+cy; a

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     Step 146: c on left = 1

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     Step 147: 3 and on the right a

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     Step 148: c = .24

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     Step 149: 30; ShrinkExpandA=2

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     Step 150: X_Offset_A=0

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     Step 151: Y_Offset_A=2

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     Step 152: ShrinkExpandB=2

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     Step 153: X_Offset_B=0

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     Step 154: Y_Offset_B=6; Formula: V=(x)/3-xy+a*(x^2+y^2)+bx+cy; a

155. 155

     Step 155: c on left = 1

156. 156

     Step 156: 3 and on the right a

157. 157

     Step 157: c = .24

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     Step 158: 30; ShrinkExpandA=2

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     Step 159: X_Offset_A=0

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     Step 160: Y_Offset_A=0

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     Step 161: ShrinkExpandB=2

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     Step 162: X_Offset_B=0

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     Step 163: Y_Offset_B=0; Butterfly catastrophe: Formula: V=x^6+ax^4+bx^3+cx^2+dx; a

164. 164

     Step 164: d on left = 1.5

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     Step 165: 2 and on the right a

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     Step 166: d = .5

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     Step 167: -.01; ShrinkExpand_1=.1

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     Step 168: X_Offset_C=2

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     Step 169: Y_Offset_C=2

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     Step 170: ShrinkExpand_2=2

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     Step 171: X_Offset_D=6

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     Step 172: Y_Offset_D=2; y on left = column L and y on right = column M;

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     Step 173: The topic is actually more involved than what is shown here and it would be a good idea to do further research to gain a better understanding of Bifurcation Theory and Catastrophe Theory

174. 174

     Step 174: as well as Chaos Theory and Lie Groups.

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     Step 175: 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

176. 176

     Step 176: Geometric and/or Trigonometric Art

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     Step 177: Charting/Diagramming and Algebraic Formulation.

Detailed Guide

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