フラクタル図形
マンデルブロート集合を描いてみました。
マンデルブロート集合の描画プログラムと色相を記述します。
プログラムは簡単に描画するため「Visual Studio」で「Visual Basic」を使用しました。
各プログラムは、基本的に同じですが、それぞれの色相を変化させるために各プログラムを
少し変化させています。
色付けには、繰返し回数を使用しています。
色相１のプログラム
１．プログラム。
kは、繰返しの計算回数です。i, jは縦横の位置です。
Public Class Form1
Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button1.Click
REM マンデルブロート１, 2016/12/06
Dim xmin, xmax, ymin, ymax As Double
Dim cr, ci, dx, dy, zr, zi, wr, wi As Double
Dim i, j, k, r, g, b As Integer
Dim gr As Graphics = PictureBox1.CreateGraphics
Dim w As Integer = PictureBox1.ClientRectangle.Width
Dim h As Integer = PictureBox1.ClientRectangle.Height
gr.Clear(PictureBox1.BackColor)
xmin = Val(TextBox1.Text)
xmax = Val(TextBox2.Text)
ymin = Val(TextBox3.Text)
ymax = Val(TextBox4.Text)
dx = (xmax - xmin) / w
dy = (ymax - ymin) / h
For i = 0 To h - 1
For j = 0 To w - 1
cr = xmin + j * dx
ci = ymin + i * dy
zr = 0
zi = 0
For k = 0 To 600
wr = zr * zr - zi * zi + cr
wi = 2 * zr * zi + ci
If (wr * wr + wi * wi > 4) Then Exit For
zr = wr : zi = wi
Next
If (k Mod 3) = 0 Then
r = 255 : g = 0 : b = 0
Else
r = k : g = k + 64 : b = k + 128
End If
gr.DrawRectangle(New Pen(ColorTranslator.FromOle(RGB(r, g, b))), j, i, 1, 1)
Next
Next
End Sub
Private Sub Button2_Click(sender As Object, e As EventArgs) Handles Button2.Click
End
End Sub
End Class
２．描画結果です。
色相２のプログラム
１．プログラム。
Public Class Form1
Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button1.Click
REM マンデルブロート２, 2016/12/06
Dim Res, Ree, Ims, Ime As Double
Dim Re, Im As Double
Dim dr, di, zr, zi As Double
Dim cr, ci As Double
Dim i, j, c, k As Integer
Dim g As Graphics = PictureBox1.CreateGraphics
Dim mybrush As New SolidBrush(Color.Black)
Dim wi As Integer = PictureBox1.ClientRectangle.Width
Dim he As Integer = PictureBox1.ClientRectangle.Height
g.Clear(PictureBox1.BackColor)
Res = Val(TextBox1.Text)
Ree = Val(TextBox2.Text)
Ims = Val(TextBox3.Text)
Ime = Val(TextBox4.Text)
dr = (Ree - Res) / wi
di = (Ime - Ims) / he
For i = 0 To he - 1
For j = 0 To wi - 1
cr = Res + j * dr
ci = Ims + i * di
zr = 0
zi = 0
For k = 0 To 600
Re = zr * zr - zi * zi + cr
Im = 2 * zr * zi + ci
If (Re * Re + Im * Im > 4) Then Exit For
zr = Re : zi = Im
Next
c = k Mod 7
Select Case c
Case 0
mybrush.Color = Color.Yellow
Case 1
mybrush.Color = Color.Magenta
Case 2
mybrush.Color = Color.Red
Case 3
mybrush.Color = Color.Lime
Case 4
mybrush.Color = Color.Pink
Case 5
mybrush.Color = Color.Gold
Case 6
mybrush.Color = Color.Black
End Select
g.FillRectangle(mybrush, j, i, 1, 1)
Next
Next
End Sub
End Class
２．描画結果です。
色相３のプログラム
１．プログラム。
Public Class Form1
Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button1.Click
REM マンデルブロート２, 2016/12/06
Dim Res, Ree, Ims, Ime As Double
Dim Re, Im As Double
Dim dr, di, zr, zi As Double
Dim cr, ci As Double
Dim i, j, c, k, r, g, b, d As Integer
Dim gr As Graphics = PictureBox1.CreateGraphics
Dim mybrush As New SolidBrush(Color.Black)
Dim wi As Integer = PictureBox1.ClientRectangle.Width
Dim he As Integer = PictureBox1.ClientRectangle.Height
gr.Clear(PictureBox1.BackColor)
Res = Val(TextBox1.Text)
Ree = Val(TextBox2.Text)
Ims = Val(TextBox3.Text)
Ime = Val(TextBox4.Text)
dr = (Ree - Res) / wi
di = (Ime - Ims) / he
For i = 0 To he - 1
For j = 0 To wi - 1
cr = Res + j * dr
ci = Ims + i * di
zr = 0
zi = 0
For k = 0 To 1023
Re = zr * zr - zi * zi + cr
Im = 2 * zr * zi + ci
If (Re * Re + Im * Im > 4) Then Exit For
zr = Re : zi = Im
Next
d = (k Mod 64) * 4
If d <= 0 Then
r = 0 : g = 0 : b = 0
Else
c = Int(d / 43)
Select Case c
Case 0
r = 255 : g = d * 5 : b = 0
Case 1
r = (88 - d) * 5 : g = 255 : b = 0
Case 2
r = 0 : g = 255 : b = (d - 86) * 5
Case 3
r = 0 : g = (172 - d) * 5 : b = 255
Case 4
r = (d - 172) * 5 : g = 0 : b = 255
Case 5
r = 255 : g = 0 : b = (255 - d) * 5
End Select
End If
gr.DrawRectangle(New Pen(ColorTranslator.FromOle(RGB(r, g, b))), j, i, 1, 1)
Next
Next
End Sub
Private Sub Button2_Click(sender As Object, e As EventArgs) Handles Button2.Click
End
End Sub
End Class
２．描画結果です。
色相４のプログラム
１．プログラム。
Public Class Form1
Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button1.Click
REM マンデルブロート２, 2016/12/06
Dim Res, Ree, Ims, Ime As Double
Dim Re, Im As Double
Dim dr, di, zr, zi As Double
Dim cr, ci As Double
Dim i, j, c, k, r, g, b, d As Integer
Dim gr As Graphics = PictureBox1.CreateGraphics
Dim mybrush As New SolidBrush(Color.Black)
Dim wi As Integer = PictureBox1.ClientRectangle.Width
Dim he As Integer = PictureBox1.ClientRectangle.Height
gr.Clear(PictureBox1.BackColor)
Res = Val(TextBox1.Text)
Ree = Val(TextBox2.Text)
Ims = Val(TextBox3.Text)
Ime = Val(TextBox4.Text)
dr = (Ree - Res) / wi
di = (Ime - Ims) / he
For i = 0 To he - 1
For j = 0 To wi - 1
cr = Res + j * dr
ci = Ims + i * di
zr = 0
zi = 0
For k = 0 To 1023
Re = zr * zr - zi * zi + cr
Im = 2 * zr * zi + ci
If (Re * Re + Im * Im > 4) Then Exit For
zr = Re : zi = Im
Next
d = (k Mod 32) * 8
c = Int(d / 42.667)
Select Case c
Case 0
r = 0 : g = d * 6 : b = 255
Case 1
r = 0 : g = 255 : b = 255 - 6 * (d - 43)
Case 2
r = 6 * (d - 86) : g = 255 : b = 0
Case 3
r = 255 : g = 255 - 6 * (d - 129) : b = 0
Case 4
r = 255 : g = 0 : b = 6 * (d - 171)
Case 5
r = 255 - 6 * (d - 214) : g = 0 : b = 255
Case Else
r = 0 : g = 0 : b = 0
End Select
gr.DrawRectangle(New Pen(ColorTranslator.FromOle(RGB(r, g, b))), j, i, 1, 1)
Next
Next
End Sub
Private Sub Button2_Click(sender As Object, e As EventArgs) Handles Button2.Click
End
End Sub
End Class
２．描画結果です。
色相５のプログラム
１．プログラム。
Public Class Form1
Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button1.Click
REM マンデルブロート２, 2016/12/06
Dim Res, Ree, Ims, Ime As Double
Dim Re, Im As Double
Dim dr, di, zr, zi As Double
Dim cr, ci As Double
Dim i, j, c, k As Integer
Dim g As Graphics = PictureBox1.CreateGraphics
Dim mybrush As New SolidBrush(Color.Black)
Dim wi As Integer = PictureBox1.ClientRectangle.Width
Dim he As Integer = PictureBox1.ClientRectangle.Height
g.Clear(PictureBox1.BackColor)
Res = Val(TextBox1.Text)
Ree = Val(TextBox2.Text)
Ims = Val(TextBox3.Text)
Ime = Val(TextBox4.Text)
dr = (Ree - Res) / wi
di = (Ime - Ims) / he
For i = 0 To he - 1
For j = 0 To wi - 1
cr = Res + j * dr
ci = Ims + i * di
zr = 0
zi = 0
For k = 0 To 600
Re = zr * zr - zi * zi + cr
Im = 2 * zr * zi + ci
If (Re * Re + Im * Im > 4) Then Exit For
zr = Re : zi = Im
Next
c = k Mod 7
Select Case c
Case 0
mybrush.Color = Color.DeepPink
Case 1
mybrush.Color = Color.Magenta
Case 2
mybrush.Color = Color.HotPink
Case 3
mybrush.Color = Color.LightPink
Case 4
mybrush.Color = Color.Pink
Case 5
mybrush.Color = Color.PeachPuff
Case 6
mybrush.Color = Color.Red
End Select
g.FillRectangle(mybrush, j, i, 1, 1)
Next
Next
End Sub
End Class
２．描画結果です。
