Subject: Re: Stereo Mandelbrot(s)

From: [email-masked] (Daniel Green)
Date: 18 Aug 92 18:51:11 GMT

In article 714122157@lillee, [email-masked] (Keven Weber) writes:
> 
> [...]
> FOZEPDKDNQLHFEJDFOZEPDKDNQLHFEJDFOZEPDKDNQLHFEJDFOZEPDKDNQLHFEJDFOZEPDKDNQLHFEJD
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> 
> 
> But I can sometimes see more than one Mandelbrot set (one inside the other).
> Depending on how I focus I can lock onto different images, each with an
> additional Mandelbrot set within it (the additional M. set floats above
> the background but below the surrounding M. sets creating a stepping effect).
> I can see at most 3 M. sets (one inside the other) floating at 3 different
> heights above the background.
> 
> Does anyone else see this?
> 
> What's going on?

At first I thought "what sort of bullshit is this?" but there really is
something to it.  Viewed cross-eyed one can see the Mandelbrot set pressed
into the background (the expected effect) but if you cross your eyes further
so that two units of overlapping occure, you can distinctly see three levels
depth.  The smallest inner one looks something like a mandlebrot set but
the next level is only two copies of the original mandlebrot set offset and
overlapping by one unit.

Cross-eyed viewing is easiest to use here because the extream shift distance
is easier to accomplish that way.  For wall-eyed viewing you will need to back
up about six to eight feet to make that possible.  The smallest inner figure then
floats above the others.

Actually, the smallest set is really just the original one with a one-unit
vertical slice removed from it's center.  I'm sure this two-step effect is an
artifact of the particular dataset, but it is certainly wierd.  It opens up
the possibility of new effects that could exploit multi-unit overlapping.  Neet!

---
Daniel Green
[email-masked]
      ___________          ___________
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      |  _________         | _________
      |  |       |         | |       |
      |  |  _______        | | _______
      |  |  |     |        | | |     |
      ---|  |  _____       --| | _____
	 ---|  | D |         --| | D |
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From: [email-masked] (Alex F. Dietz)
Date: 18 Aug 92 22:06:03 GMT

In article [email-masked], [email-masked] (Daniel Green) writes:
> > [ASCII mandelbrot deleted.]
> > 
> > 
[Most of next text deleted]
 
> the possibility of new effects that could exploit multi-unit overlapping.  Neet!

Weird.  This effect works with the postscript sirds as well.  It appears
to be an property of all sirds.  Just as the original 3d layers arise when the
2d images are merged by your eyes, the "extra" layers arise at the intersection
of the original 3d image by further divergence of the eyes.  What you see are
two identical 3d images side by side & overlapping each other, but where they
overlap additional depth is perceived.  Cool stuff!

-A Dietz
Bellcore, Morristown

---

From: [email-masked] (Keven Weber)
Date: 18 Aug 92 07:15:57 GMT

[email-masked] (Ben Davenport) writes:

>>Here is a stereo image of a Mandelbrot set.  It was created using
>>stereogram.c.  The source file was created with a c program that
>>generates a text mandelbrot set (so it's not just a guess as to
>>what the set looks like.)  When viewed cross-eyed, the set appears
>>to float above the background. 

What's going on?

--
Email: [email-masked]

---

From: [email-masked]
Date: 19 Aug 92 16:07:35 GMT

>> FOZEPDKDNQLHFEJDFOZEPDKDNQLHFEJDFOZEPDKDNQLHFEJDFOZEPDKDNQLHFEJDFOZEPDKDNQLHFEJD
.
.
.
> the possibility of new effects that could exploit multi-unit overlapping.  Neet!

This is not just in this case though. I was always wide-eyed, until I practiced
cross-eyed, and found cross-eyed easier to focus. So out came the RDS'es, and
the above effect could be reproduced in every RDS. Normal is with 3 triangles,
next is two overlapping images (four equidistant triangles), etc ...

Anyone know what's going on ? :)

Trevor Phillips
[email-masked]

---

From: [email-masked] (Daniel Green)
Date: 20 Aug 92 17:20:27 GMT

> Anyone know what's going on ? :)

Sorry,  I should have said "two-step mandlebrot effect" because sure, the
multi-step effect will occure with any stereogram as long as it has enough
repeating base units.  It's just a coincidence that the results in this case
resemble mandlebrot sets.  (How fractal can you get?!)

---
Daniel Green
[email-masked]
      ___________          ___________
      |         |          |         |
      |  _________         | _________
      |  |       |         | |       |
      |  |  _______        | | _______
      |  |  |     |        | | |     |
      ---|  |  _____       --| | _____
         ---|  | D |         --| | D |
            ---|  G|           --|  G|
               -----             -----