c# for循环中的数组产生相同的随机整数值

这是我第一次发帖。希望这个问题不会让你太困惑。我正在为一本c#初学者的书做实验，现在卡住了。我在创建一个"模拟狗比赛"程序。当我点击"Start Race"按钮时，狗会随着计时器的每一次滴答(1到30之间的随机整数)向右移动，直到到达终点。我试过以不同的方式切换代码，阅读数组，Random类和在线for循环，但出于某种原因，无论如何，狗总是以相同的速度移动。它们需要以不同的随机速率移动。

一个解决方案会很好，但我真正想知道的是，为什么我的代码不工作?每个狗不应该被分配一个不同的随机数，因为它通过数组的"i"值循环?

图片可以在这里找到:http://makingspidersense.com/dograce.png

下面是Form1代码:

Greyhound[] dogs = new Greyhound[4];
    private void startRaceButton_Click(object sender, EventArgs e)
    {
        timer1.Start();
        dogs[0] = new Greyhound() { MyPictureBox = dog1PictureBox };
        dogs[1] = new Greyhound() { MyPictureBox = dog2PictureBox };
        dogs[2] = new Greyhound() { MyPictureBox = dog3PictureBox };
        dogs[3] = new Greyhound() { MyPictureBox = dog4PictureBox };
    }
    private void timer1_Tick(object sender, EventArgs e)
    {
        for (int i = 0; i < 4 ; i++)
        {
            if (dogs[i] != null)
            {
                dogs[i].Randomizer = new Random();
                dogs[i].Distance = dogs[i].Randomizer.Next(1, 30);
                dogs[i].Move(); 
            }
        }
    }

这是Greyhound的类代码:

class Greyhound
{
    public PictureBox MyPictureBox; 
    public bool GoingForward = true;
    public Random Randomizer; 
    public int Distance;
    public void Move() 
    {
        if (MyPictureBox != null)
        {
            if (GoingForward == true)
            {
                MyPictureBox.Left += Distance; 
                if (MyPictureBox.Left >= MyPictureBox.Parent.Width - MyPictureBox.Width)
                {
                    GoingForward = false; 
                }
            }
        }
    }
}

var r = new Random();
for (int i = 0; i < 4 ; i++)
    {
        if (dogs[i] != null)
        {
            dogs[i].Randomizer = r;
            dogs[i].Distance = r.Next(1, 30);
            dogs[i].Move(); 
        }
    }