How to understand autocorrelations caused by seeding a RNG too much?

Question

In response to this question I ran the following VBA experiment:

Sub Test()
    Dim i As Long, A As Variant
    Dim count1 As Long, count2 As Long
    ReDim A         


        

Answer 1

Partial answer only, fell free to edit and complete.

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Well, there is clearly a correlation when you overuse the Randomize function.

I tried the following code, with a conditional formatting (black fill for values >0.5), and there is clearly patterns appearing (try to comment the Randomize to see a more "random" pattern. (best seen with 20 pt columns and 10% zoom)

Function Rndmap()
    Dim i As Long, j As Long
    Dim bmp(1 To 512, 1 To 512) As Long
    For i = 1 To 512
        For j = 1 To 512
            ' Rnd -1 ' uncomment this line to get a big white and black lines pattern.
            Randomize 'comment this line to have a random pattern
            bmp(i, j) = IIf(Rnd() < 0.5, 0, 1)
        Next j
    Next i
    Range(Cells(1, 1), Cells(512, 512)) = bmp
End Function

So while the MSDN states that "Using Randomize with the same value for number does not repeat the previous sequence.", implying that if the Timer returns twice the same value, the Rnd should keep on the same random sequence without reseting, there is still some behind the scene link..

Some screenshots:

Rnd() only:

Using Randomize:

Using Rnd -1 and Randomize: