Mandelbrot distance estimation problem

[Iariak]

So I tried to implement distance estimation into my VBA program because I really liked the images you can get with that (been doing everything using escape time so far).

However, because my idea of what derivation is is extremely vague (and from what I understand, it is used in distance estimation) I ended up ripping the extra code needed for DE off of another thread on this forum (namely this one: http://www.fractalforums.com/mandelbrot-and-julia-set/problem-with-mandelbrot-distance-estimator/)

here is my code:

Code:

Sub render()

For i = -2 To 2 Step 0.01
    counteri = counteri + 1
    counterj = 0
    DoEvents
    For j = -2 To 2 Step 0.01
        counterj = counterj + 1
        iterate = iterateM(i, j)
        Cells(counteri, counterj).Interior.Color = RGB(iterate, iterate, iterate)
    Next j
Next i

End Sub

Function iterateM(ByVal j0 As Double, ByVal i0 As Double) As Long


For k = 1 To 200
    iDer = 2 * (i * iDerz - j * jDerz) + 1
    jDer = 2 * (i * jDerz + j * iDerz)
    iDerz = iDer
    jDerz = jDer
    
    i = iz * iz - (jz * jz) + i0
    j = 2 * iz * jz + j0
    iz = i
    jz = j
    mag = Sqr(i * i + j * j)
    If mag > 2 Then
        dr = Sqr(iDer * iDer + jDer * jDer)
        dist = mag * Log(mag) / dr
        patri = dist * 500
        Exit For
    End If
Next k
iterateM = patri
End Function

Now it kinda works, this is one of the pictures I was able to get with that
Mandelbrot set zoom
What bothers me though that if that image was darker, there would be visible "straps" just like the ones you get with escape time, you can see that on this image (this is the whole set)
Whole Mandelbrot using DE

If anyone has any idea what I did wrong, let me know please. Thanks!

[quaz0r]

i dont know if it is your only problem but try a larger bailout

[Iariak]

Naw man, 200 is enough for the whole set. The picture is so dark just because I wanted the straps to be visible. If it was brighter, it would look just fine. Thanks for taking your time to go through the code though

[quaz0r]

i wasnt asking, i was telling.  also your bailout in that code is 2, not 200.   i guess 200 is your maxiter there.   

[Adam Majewski]

IMHO problem is int the code which computes color from distance estimation.
Try to chang coloring :
* if interior then red
* if exterior
** if distance < 10*pixel_size then black
** else white

Show result

HTH

BTW
https://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/demm

[quaz0r]

well, the code is obviously just a basic (pun intended?) example in any case.  his question though,

if that image was darker, there would be visible "straps"

relates to his intentionally using a larger multiplier (500 instead of your suggested 10).
and again, i suspect if his bailout matched or exceeded this value it could produce better results.

[claude]

Like quaz0r said, you need to change "If mag > 2" to increase the escape radius. Attached is a comparison, showing that the "straps" reduce when the radius is increased, no harm going huge like R = 1e6 or so because once it escapes 2 it grows very fast.  The bigger the radius, the more accurate the distance estimate.

[Iariak]

Oh sorry I didn't know that number was called a bailout and assumed you meant the max iterations x) Anyway that was totally it! It would never occur to me that changing that number would have any effect, I always used 2. Anyway thanks a bunch to all of you, it works beautifully.