1. Function Formula ⚓︎

Heart-Shaped Function Formula

y=(x2)13+0.9⋅(3.3−x2)12⋅sin⁡(nπx)y = \left(x^2\right)^{\frac{1}{3}} + 0.9 \cdot \left(3.3 - x^2\right)^{\frac{1}{2}} \cdot \sin(\mathbf{n} \pi x)

where n is a parameter, and the function graph changes as the value of n changes. The domain of the function is: [-1.81, 1.81]

2. Interactive Online Demo ⚓︎

Heart-shaped function graph
y = (x²)^(1/3) + 0.9 · (3.3 - x²)^(1/2) · sin(nπx)
Parameter n value 0.0
n = 0.0

3. Implementation in Excel ⚓︎

3.1 Step-by-Step Guide ⚓︎

  1. Variable x
    1. Create a new Excel spreadsheet, and enter X and Y in cells A1 and B1 respectively;
    2. Enter -1.81 in cell A2 (the left endpoint of the domain);
    3. Select cell A2, go to the Home tab, then find Editing → Fill → Series, open the dialog, select series in Columns, set step value to 0.01, and stop value to 1.81 (the right endpoint of the domain);
    4. This generates all possible values of the variable x for the function in column A.
  1. Variable y
    1. Enter the formula in cell B2: =(A2^2)^(1/3)+0.9*(3.3-A2^2)^(1/2)*SIN($D$2*PI()*A2), where cell D2 is the parameter n, and $D$2 is an absolute reference (F4 key);
    2. Select cell B2, move the mouse to the bottom-right corner of cell B2 until the pointer changes to a black cross (fill handle), then double-click the left mouse button to auto-fill the formula downward and calculate the corresponding y values for column A.
Formula
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=(A2^2)^(1/3)+0.9*(3.3-A2^2)^(1/2)*SIN($D$2*PI()*A2)
  1. Create the Chart
    1. Select cell A1, press Ctrl + Shift + →, then press Ctrl + Shift + ↓ to select all data in columns A and B;
    2. Go to the Insert tab, find Charts → Insert Scatter (X, Y) or Bubble Chart → Scatter with Smooth Lines to create a heart-shaped scatter chart;
    3. Click the X-axis in the chart and press Delete to remove it; click the Y-axis and press Delete to remove it; also delete the chart title and legend.
  1. Iterative Calculation
    1. Enter the formula =D2+0.1 in cell D2 and press Enter;
    2. Select cell D2, click the File tab in the top-left corner of Excel, then select More → Options → Formulas at the bottom left;
    3. Under the Calculation options section on the right, check Enable iterative calculation, set Maximum iterations to 1, and click OK to save the settings;
    4. Hold down the F9 key (or Fn + F9 key) on the keyboard, and the heart-shaped function graph will begin a “beating” animation effect.

Result:

3.2 Excel Macro Code for Calculation Control ⚓︎

  • Open your Excel file, click the File tab in the top-left corner, select Save As, and set the save type to: Excel Macro-Enabled Workbook (*.xlsm).
  • Click the File tab in the top-left corner, select More → Options → Customize Ribbon at the bottom left, check Developer under Customize the Ribbon on the right, and click OK to save.

(1) Form Control: Button ⚓︎

Click Developer, then click Visual Basic, and enter the following code:

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Public isLooping As Boolean
Public i As Double

Sub 心形图()
    isLooping = Not isLooping
    If isLooping Then
        i = 0
        Do While isLooping And i <= 1000
            Range("D2").Value = i / 10
            i = i + 1
            DoEvents
            If i Mod 1 = 0 Then
                DoEvents
            End If
        Loop
        isLooping = False
    End If
End Sub

Insert a Form Control: Button, assign the macro 心形图 to it, click OK, and name the button 开关.

(2) Form Control: Start Button and Continuous Toggle ⚓︎

Click Developer, then click Visual Basic, and enter the following code:

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Public isLooping As Boolean
Public i As Double
Public continue As Boolean

Sub 心形图()
    isLooping = Not isLooping
    If isLooping Then
        If Not continue Then
            i = 0
        End If
        Do While isLooping And i <= 1000
            Range("D2").Value = i / 10
            i = i + 1
            DoEvents
            If i Mod 1 = 0 Then
                DoEvents
            End If
        Loop
        isLooping = False
    End If
End Sub

Sub 连续开关()
    continue = Not continue
End Sub

Insert a Form Control: Button, assign the macro 心形图 to it, click OK, and name the button 启动开关 for controlling start/stop;
Insert a Form Control: Button, assign the macro 连续开关 to it, click OK, and name the button 连续开关 for controlling whether parameter n runs continuously.

(3) ActiveX Control: Button ⚓︎

Insert an ActiveX Control: Button, enable Design Mode under the Developer tab, right-click the newly created button, select View Code, and enter the following code:

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Public isLooping As Boolean
Public i As Double

Private Sub CommandButton1_Click()
    isLooping = Not isLooping
    If isLooping Then
        CommandButton1.Caption = "停止"
        i = 0
        Do While isLooping And i <= 1000
            Range("D2").Value = i / 10
            i = i + 1
            DoEvents
            If i Mod 1 = 0 Then
                DoEvents
            End If
        Loop
        isLooping = False
        CommandButton1.Caption = "Start"
    Else
        isLooping = False
        CommandButton1.Caption = "Start"
    End If
End Sub

(4) Form Control: Scroll Bar ⚓︎

Insert a Form Control: Scroll Bar, right-click the scroll bar, select Format Control, and under the Control tab, set Minimum value: 0, Maximum value: 100, Incremental change: 1, and Cell link: $D$2.

(5) ActiveX Control: Scroll Bar ⚓︎

Insert an ActiveX Control: Scroll Bar, enable Design Mode under the Developer tab, right-click the newly created scroll bar, select View Code, and enter the following code:

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Private Sub ScrollBar1_Change()
Range("D2") = ScrollBar1.Value / 10
End Sub

4. File Download ⚓︎

Click to Download