Public Class Form1
    Private img As New Bitmap(500, 250)
    Private gf As Graphics
    'Private A0 As Double = 1
    Dim MinA As Double, MaxA As Double, dM As Double
    Dim A As Double, DA As Double, H As Integer, W As Integer

    Private Sub drawGrad() '目盛表示
        Dim X As Double, IX As Integer, HH As Integer = H \ 10, i As Integer
        Dim P1 As Pen = New Pen(Color.Gray), P2 As Pen = New Pen(Color.Black)
        For i = 1 To 9
            If (i Mod 5) = 0 Then
                gf.DrawLine(P2, 0, i * HH, W, i * HH)
            Else
                gf.DrawLine(P1, 0, i * HH, W, i * HH)
            End If
        Next
          X = 0.0 : i = 0
        Do While X < MaxA
            X = X + dM : i = i + 1
            If X > MinA Then
                IX = (X - MinA) / (MaxA - MinA) * W
                If IX >= 0 And IX < W Then
                    If (i Mod 5) = 0 Then
                        gf.DrawLine(P2, IX, 0, IX, 254)
                    Else
                        gf.DrawLine(P1, IX, 0, IX, 254)
                    End If
                End If
            End If
        Loop      
    End Sub
    Private Sub initData()
        gf = Graphics.FromImage(img) : gf.Clear(Color.White) '描画クリア
        MinA = Val(TextBox1.Text)
        MaxA = Val(TextBox2.Text)
        dM = Val(TextBox3.Text)
        A = MinA : DA = (MaxA - MinA) / 200000
        H = img.Height : W = img.Width
    End Sub
    Private Sub drawMap()
        Dim i As Integer, IX As Integer, IY As Integer, X As Double
        drawGrad()
        X = 0.1
        For i = 1 To 200000
            IY = H - X * H + 0.5 : IX = (A - MinA) / (MaxA - MinA) * W + 0.5
            If IX >= 0 And IX < W And IY >= 0 And IY < H Then img.SetPixel(IX, IY, Color.Blue)
            X = A * X * (1 - X) : A = A + DA
        Next
        PictureBox1.Image = img : gf.Dispose() 'リソースを解放する
    End Sub
    Private Sub Button1_Click(sender As System.Object, e As System.EventArgs) Handles Button1.Click
        initData() : drawMap()
    End Sub
End Class