Re: A89: Seven level Grayscale

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Re: A89: Seven level Grayscale


On Sat, 29 Jul 2000, Scott Noveck wrote:

> 
> > Btw, I recently tested my method with 8 levels gray, and it worked realy
> > good, just an itty bity more flicker. I won't post that since it is such a
> > simple mod. (If someones wonders I used plane sequence: 0102010.)
> 
> That's not 8 level, it's still seven.  Setting one and two is the same as
> setting just zero.  

Let's take a close look at the sequence given above.  Plane 0 is shown 4
times, plane 1 is shown 2 times.

So, setting 1 and 2 makes a plane show 3 times per cycle.  Setting just 0
of course is shown 4 times per cycle.

Thus, your reasoning allows us to clearly establish that 3 = 4.  This
method of grayscale analysis certainly will open a new era in mathematics. 

> [...]
> 
> 8 level requires 4 displays of one plane, 3 of another, and two of the final
> plane.
> 
> The number of planes required for any arbitrary level L is log base two of
> L, rounded up.  To achieve the maximum number of levels for any arbitrary
> number of planes P will have the P spans of time be the P consecutive
> integers with the lowest number being (P-1).

Since you said these are arbitrary numbers, presumably P could be the
number 4.  From the logarithm stuff, we can see that 16 is the maximum
number of colors for this plane.  From the consecutive integers stuff, we
can tell that the number of times each plane must be shown is as follows:

Plane 0: 6
Plane 1: 5
Plane 2: 4
Plane 3: 3

Now, all combinations of planes must be different to have the maximum
number of colors.  So, setting planes 1 and 2 only must not be the same
color as setting planes 0 and 3 only.  Thus, the total time each would be
different.  Thus we can determine that

6 + 3  isn't equal to  5 + 4

Unfortunately, there's no answer as to exactly what those things are equal
to in this post.  Clearly this brilliant new way of analysis developed
here needs to be pursued further.

Strangely enough, I had all along been assuming that the maximum number of
colors for P planes could be given by showing the least significant plane
one time, then two times for the next plane, up to 2 ^ (P - 1) for the
most significant plane.  As this would simply make the number of times per
complete cycle a pixel was shown equal to the binary number made by
pulling bits from the planes, I thought that would guarantee that 2 ^ P
possible colors would exist.  But it's a good thing that Scott Noveck has
shown me the error of my ways.

We all must bow down to Scott's new mathematical insights, and curse
foolish people who think they can do what he has shown to be impossible.
References: