LINE - Hilbert curves

I wrote an image processing program some time ago to explore the effect
of replacing raster scanning with Hilbert curve scanning, and a side
effect of this work was a little program that generates hilbert curves:

% filltest 2 2
._.
._!
%
% filltest 4 4
. ._._.
!_! ._!
._. !_.
! !_._!
%
% filltest 8 8
._. ._._. ._._.
._! !_. !_! ._!
! ._. ! ._. !_.
!_! !_! ! !_._!
._. ._. ! ._._.
! !_! ! !_! ._!
!_. ._! ._. !_.
._! !_._! !_._!
%
% filltest 16 16
. ._._. ._._. ._._. ._._. ._._.
!_! ._! !_. !_! ._! !_. !_! ._!
._. !_. ._! ._. ! ._. ! ._. !_.
! !_._! !_._! ! !_! !_! ! !_._!
!_. ._._._. ._! ._. ._. ! ._._.
._! !_. ._! !_. ! !_! ! !_! ._!
! ._. ! ! ._. ! !_. ._! ._. !_.
!_! !_! !_! !_! ._! !_._! !_._!
._. ._. ._. ._. !_. ._._. ._._.
! !_! ! ! !_! ! ._! !_. !_! ._!
!_. ._! !_. ._! ! ._. ! ._. !_.
._! !_._._! !_. !_! !_! ! !_._!
! ._._. ._._. ! ._. ._. ! ._._.
!_! ._! !_. !_! ! !_! ! !_! ._!
._. !_. ._! ._. !_. ._! ._. !_.
! !_._! !_._! !_._! !_._! !_._!
%
% filltest 32 32
._. ._._. ._._. ._._. ._._. ._._. ._._. ._._. ._._. ._._. ._._.
._! !_. !_! ._! !_. !_! ._! !_. !_! ._! !_. !_! ._! !_. !_! ._!
! ._. ! ._. !_. ._! ._. ! ._. ! ._. !_. ._! ._. ! ._. ! ._. !_.
!_! !_! ! !_._! !_._! ! !_! !_! ! !_._! !_._! ! !_! !_! ! !_._!
._. ._. ! ._._. ._._. ! ._. ._. !_. ._._._. ._! ._. ._. ! ._._.
! !_! ! !_! ._! !_. !_! ! !_! ! ._! !_. ._! !_. ! !_! ! !_! ._!
!_. ._! ._. !_. ._! ._. !_. ._! ! ._. ! ! ._. ! !_. ._! ._. !_.
._! !_._! !_._! !_._! !_._! !_. !_! !_! !_! !_! ._! !_._! !_._!
! ._._. ._._. ._. ._._. ._._. ! ._. ._. ._. ._. !_. ._._. ._._.
!_! ._! !_. !_! !_! ._! !_. !_! ! !_! ! ! !_! ! ._! !_. !_! ._!
._. !_. ._! ._. ._. !_. ._! ._. !_. ._! !_. ._! ! ._. ! ._. !_.
! !_._! !_._! ! ! !_._! !_._! ! ._! !_._._! !_. !_! !_! ! !_._!
!_. ._._._. ._! !_. ._._._. ._! ! ._._. ._._. ! ._. ._. ! ._._.
._! !_. ._! !_. ._! !_. ._! !_. !_! ._! !_. !_! ! !_! ! !_! ._!
! ._. ! ! ._. ! ! ._. ! ! ._. ! ._. !_. ._! ._. !_. ._! ._. !_.
!_! !_! !_! !_! !_! !_! !_! !_! ! !_._! !_._! !_._! !_._! !_._!
._. ._. ._. ._. ._. ._. ._. ._. ! ._._. ._._. ._._. ._._. ._._.
! !_! ! ! !_! ! ! !_! ! ! !_! ! !_! ._! !_. !_! ._! !_. !_! ._!
!_. ._! !_. ._! !_. ._! !_. ._! ._. !_. ._! ._. ! ._. ! ._. !_.
._! !_._._! !_. ._! !_._._! !_. ! !_._! !_._! ! !_! !_! ! !_._!
! ._._. ._._. ! ! ._._. ._._. ! !_. ._._._. ._! ._. ._. ! ._._.
!_! ._! !_. !_! !_! ._! !_. !_! ._! !_. ._! !_. ! !_! ! !_! ._!
._. !_. ._! ._. ._. !_. ._! ._. ! ._. ! ! ._. ! !_. ._! ._. !_.
! !_._! !_._! !_! !_._! !_._! ! !_! !_! !_! !_! ._! !_._! !_._!
!_. ._._. ._._. ._._. ._._. ._! ._. ._. ._. ._. !_. ._._. ._._.
._! !_. !_! ._! !_. !_! ._! !_. ! !_! ! ! !_! ! ._! !_. !_! ._!
! ._. ! ._. !_. ._! ._. ! ._. ! !_. ._! !_. ._! ! ._. ! ._. !_.
!_! !_! ! !_._! !_._! ! !_! !_! ._! !_._._! !_. !_! !_! ! !_._!
._. ._. ! ._._. ._._. ! ._. ._. ! ._._. ._._. ! ._. ._. ! ._._.
! !_! ! !_! ._! !_. !_! ! !_! ! !_! ._! !_. !_! ! !_! ! !_! ._!
!_. ._! ._. !_. ._! ._. !_. ._! ._. !_. ._! ._. !_. ._! ._. !_.
._! !_._! !_._! !_._! !_._! !_._! !_._! !_._! !_._! !_._! !_._!
%
% filltest 19 9
._. ._._. ._._. ._._. ._._. ._._. ._.
._! !_. !_! ._! !_. !_! ._! !_. !_! !
! ._. ! ._. !_. ._! ._. ! ._. ! ._. !
!_! !_! ! !_._! !_._! ! !_! !_! ! !_!
._. ._. ! ._._. ._._. ! ._. ._. !_. .
! !_! ! !_! ._! !_. !_! ! !_! ! ._! !
!_. ._! ._. !_. ._! ._. !_. ._! ! ._.
._! !_._! !_._! !_._! !_._! !_. !_! !
!_._._._._._._._._._._._._._._! ._._.
%
The final example above shows that the program does some odd things
when you ask it to fill a region that isn't a power-of-two square,
but what it does, in that case, didn't matter in the least for my
data compression application.

				Doug Jones
				jon...@cs.uiowa.edu

In article <2t2slh$mt...@mailhost.interaccess.com> jon...@pyrite.cs.uiowa.edu (Douglas W. Jones,201H MLH,3193350740,3193382879) writes:
>I wrote an image processing program some time ago to explore the effect
>of replacing raster scanning with Hilbert curve scanning, and a side
>effect of this work was a little program that generates hilbert curves:

[nice hilbert curves clipped]

... is the source available? And how about replacing the dots (.) with 
underlines (_) and the exclamation-marks (!) with bars (|). So a hilbert 
would look like this:

Old version:

% filltest 8 8
._. ._._. ._._.
._! !_. !_! ._!
! ._. ! ._. !_.
!_! !_! ! !_._!
._. ._. ! ._._.
! !_! ! !_! ._!
!_. ._! ._. !_.
._! !_._! !_._!

New version:

% filltest 8 8
___ _____ _____
__| |__ |_| __|
| ___ | ___ |__
|_| |_| | |___|
___ ___ | _____
| |_| | |_| __|
|__ __| ___ |__
__| |___| |___|

... i think the visible effect will be much stronger. But nonetheless, i'd be 
interested in the source for the program.



--

                .odbo.
            .od88888888bo.                  Paul Foerster
        .od8888888888888888bo.
    .od888888888888888888888888bo.          pau...@heino.ibh.rwth-aachen.de
 od88888888888888888888888888888888bo
  `~888888888888888888888888888888~'
     `~888888888888888888888888~'|          "Beam me up Scotty, there's no
        `~888888888888888888~'   |              intelligent life down here!"
          |`~888888888888~'|     |
          \   `~888888~'   /     A
           `-_   `~~'   _-'      H
              `--____--'

Those hilbert curves were really messed up in transmission over the net!
The problem is that a leading period gets translated to two leading
periods to defeat something somewhere, and the result was hash.  Never
start a line with a dot if you want your ASCII ART to survive the net!

Here is a corrected version of my posting:

I wrote an image processing program some time ago to explore the effect
of replacing raster scanning with Hilbert curve scanning, and a side
effect of this work was a little program that generates hilbert curves:

 % filltest 2 2
 ._.
 ._!
 %
 % filltest 4 4
 . ._._.
 !_! ._!
 ._. !_.
 ! !_._!
 %
 % filltest 8 8
 ._. ._._. ._._.
 ._! !_. !_! ._!
 ! ._. ! ._. !_.
 !_! !_! ! !_._!
 ._. ._. ! ._._.
 ! !_! ! !_! ._!
 !_. ._! ._. !_.
 ._! !_._! !_._!
 %
 % filltest 16 16
 . ._._. ._._. ._._. ._._. ._._.
 !_! ._! !_. !_! ._! !_. !_! ._!
 ._. !_. ._! ._. ! ._. ! ._. !_.
 ! !_._! !_._! ! !_! !_! ! !_._!
 !_. ._._._. ._! ._. ._. ! ._._.
 ._! !_. ._! !_. ! !_! ! !_! ._!
 ! ._. ! ! ._. ! !_. ._! ._. !_.
 !_! !_! !_! !_! ._! !_._! !_._!
 ._. ._. ._. ._. !_. ._._. ._._.
 ! !_! ! ! !_! ! ._! !_. !_! ._!
 !_. ._! !_. ._! ! ._. ! ._. !_.
 ._! !_._._! !_. !_! !_! ! !_._!
 ! ._._. ._._. ! ._. ._. ! ._._.
 !_! ._! !_. !_! ! !_! ! !_! ._!
 ._. !_. ._! ._. !_. ._! ._. !_.
 ! !_._! !_._! !_._! !_._! !_._!
 %
 % filltest 32 32
 ._. ._._. ._._. ._._. ._._. ._._. ._._. ._._. ._._. ._._. ._._.
 ._! !_. !_! ._! !_. !_! ._! !_. !_! ._! !_. !_! ._! !_. !_! ._!
 ! ._. ! ._. !_. ._! ._. ! ._. ! ._. !_. ._! ._. ! ._. ! ._. !_.
 !_! !_! ! !_._! !_._! ! !_! !_! ! !_._! !_._! ! !_! !_! ! !_._!
 ._. ._. ! ._._. ._._. ! ._. ._. !_. ._._._. ._! ._. ._. ! ._._.
 ! !_! ! !_! ._! !_. !_! ! !_! ! ._! !_. ._! !_. ! !_! ! !_! ._!
 !_. ._! ._. !_. ._! ._. !_. ._! ! ._. ! ! ._. ! !_. ._! ._. !_.
 ._! !_._! !_._! !_._! !_._! !_. !_! !_! !_! !_! ._! !_._! !_._!
 ! ._._. ._._. ._. ._._. ._._. ! ._. ._. ._. ._. !_. ._._. ._._.
 !_! ._! !_. !_! !_! ._! !_. !_! ! !_! ! ! !_! ! ._! !_. !_! ._!
 ._. !_. ._! ._. ._. !_. ._! ._. !_. ._! !_. ._! ! ._. ! ._. !_.
 ! !_._! !_._! ! ! !_._! !_._! ! ._! !_._._! !_. !_! !_! ! !_._!
 !_. ._._._. ._! !_. ._._._. ._! ! ._._. ._._. ! ._. ._. ! ._._.
 ._! !_. ._! !_. ._! !_. ._! !_. !_! ._! !_. !_! ! !_! ! !_! ._!
 ! ._. ! ! ._. ! ! ._. ! ! ._. ! ._. !_. ._! ._. !_. ._! ._. !_.
 !_! !_! !_! !_! !_! !_! !_! !_! ! !_._! !_._! !_._! !_._! !_._!
 ._. ._. ._. ._. ._. ._. ._. ._. ! ._._. ._._. ._._. ._._. ._._.
 ! !_! ! ! !_! ! ! !_! ! ! !_! ! !_! ._! !_. !_! ._! !_. !_! ._!
 !_. ._! !_. ._! !_. ._! !_. ._! ._. !_. ._! ._. ! ._. ! ._. !_.
 ._! !_._._! !_. ._! !_._._! !_. ! !_._! !_._! ! !_! !_! ! !_._!
 ! ._._. ._._. ! ! ._._. ._._. ! !_. ._._._. ._! ._. ._. ! ._._.
 !_! ._! !_. !_! !_! ._! !_. !_! ._! !_. ._! !_. ! !_! ! !_! ._!
 ._. !_. ._! ._. ._. !_. ._! ._. ! ._. ! ! ._. ! !_. ._! ._. !_.
 ! !_._! !_._! !_! !_._! !_._! ! !_! !_! !_! !_! ._! !_._! !_._!
 !_. ._._. ._._. ._._. ._._. ._! ._. ._. ._. ._. !_. ._._. ._._.
 ._! !_. !_! ._! !_. !_! ._! !_. ! !_! ! ! !_! ! ._! !_. !_! ._!
 ! ._. ! ._. !_. ._! ._. ! ._. ! !_. ._! !_. ._! ! ._. ! ._. !_.
 !_! !_! ! !_._! !_._! ! !_! !_! ._! !_._._! !_. !_! !_! ! !_._!
 ._. ._. ! ._._. ._._. ! ._. ._. ! ._._. ._._. ! ._. ._. ! ._._.
 ! !_! ! !_! ._! !_. !_! ! !_! ! !_! ._! !_. !_! ! !_! ! !_! ._!
 !_. ._! ._. !_. ._! ._. !_. ._! ._. !_. ._! ._. !_. ._! ._. !_.
 ._! !_._! !_._! !_._! !_._! !_._! !_._! !_._! !_._! !_._! !_._!
 %
 % filltest 19 9
 ._. ._._. ._._. ._._. ._._. ._._. ._.
 ._! !_. !_! ._! !_. !_! ._! !_. !_! !
 ! ._. ! ._. !_. ._! ._. ! ._. ! ._. !
 !_! !_! ! !_._! !_._! ! !_! !_! ! !_!
 ._. ._. ! ._._. ._._. ! ._. ._. !_. .
 ! !_! ! !_! ._! !_. !_! ! !_! ! ._! !
 !_. ._! ._. !_. ._! ._. !_. ._! ! ._.
 ._! !_._! !_._! !_._! !_._! !_. !_! !
 !_._._._._._._._._._._._._._._! ._._.
 %
The final example above shows that the program does some odd things
when you ask it to fill a region that isn't a power-of-two square,
but what it does, in that case, didn't matter in the least for my
data compression application.

				Doug Jones
 				jon...@cs.uiowa.edu

From article <2t4ro1$bi...@gagme.wwa.com>,
by pau...@heino.ibh.rwth-aachen.de (Paul Foerster):
> 
> ... is the source available?

E-mail your requests to me, I'll E-mail C source to you.

> ... And how about replacing the dots (.) with underlines (_) and the
> exclamation-marks (!) with bars (|)...

My original used _ and |, but it looked better with a strong mark at
each vertex.  Periods (.) worked well, and if your exclamation point
prints heavy, with the dot at the bottom as sharp as the period, it
looks very good.  Note that my original posting was corrupted by a
"feature" of the net that lines starting with a period get it doubled
to defeat something or another somewhere.  The example should have
looked like this:

 % filltest 8 8
  ._. ._._. ._._.
  ._! !_. !_! ._!
  ! ._. ! ._. !_.
  !_! !_! ! !_._!
  ._. ._. ! ._._.
  ! !_! ! !_! ._!
  !_. ._! ._. !_.
  ._! !_._! !_._!

Which, in my eyes, looks pretty good, I think better than your proposed:
> ___ _____ _____
> __| |__ |_| __|
> | ___ | ___ |__
> |_| |_| | |___|
> ___ ___ | _____
> | |_| | |_| __|
> |__ __| ___ |__
> __| |___| |___|

The problem with limiting yourself to | and _ is that the _ hangs over the
end of each corner, looking a bit sloppy.

				Doug Jones
				jon...@cs.uiowa.edu

+--- Douglas W. Jones <jon...@pyrite.cs.uiowa.edu> writes:
| 
| >From article <2t4ro1$bi...@gagme.wwa.com>,
| by pau...@heino.ibh.rwth-aachen.de (Paul Foerster):
| > ... And how about replacing the dots (.) with underlines (_) and the
| > exclamation-marks (!) with bars (|)...
| 
| My original used _ and |, but it looked better with a strong mark at
| each vertex.  Periods (.) worked well, and if your exclamation point
| prints heavy, with the dot at the bottom as sharp as the period, it
| looks very good.
|  {snip}
| The problem with limiting yourself to | and _ is that the _ hangs over the
| end of each corner, looking a bit sloppy.

True... but on my terminal (fairly standard PC character set), the 
exclamation point is *too* heavy--the bulbous part at the top makes the 
vertical lines jump out to the exclusion of the horizontal ones.

Replacing non-corner periods with underscores and replacing the
exclamation points with pipes seems to work well: 

 ._. .___. .___.
 ._| |_. |_| ._|
 | ._. | ._. |_.
 |_| |_| | |___|
 ._. ._. | .___.
 | |_| | |_| ._|
 |_. ._| ._. |_.
 ._| |___| |___|

If you don't mind rounding off the corners, you can drop the periods 
alltogether for what feels, to my eye, slightly less jumpy:
  _   ___   ___
  _| |_  |_|  _|
 |  _  |  _  |_
 |_| |_| | |___|
  _   _  |  ___
 | |_| | |_|  _|
 |_   _|  _  |_
  _| |___| |___|

Previous renderings preserved for comparison:

|   ._. ._._. ._._.
|   ._! !_. !_! ._!
|   ! ._. ! ._. !_.
|   !_! !_! ! !_._!
|   ._. ._. ! ._._.
|   ! !_! ! !_! ._!
|   !_. ._! ._. !_.
|   ._! !_._! !_._!
| 
| > ___ _____ _____
| > __| |__ |_| __|
| > | ___ | ___ |__
| > |_| |_| | |___|
| > ___ ___ | _____
| > | |_| | |_| __|
| > |__ __| ___ |__
| > __| |___| |___|

Strictly IMHO and WMHE (With My Humble Eyes), of course.

(By-the-by, I'm quite enjoying the new rec group.  I don't have time any
more to keep up with the volume that passes through a.a-a anymore... this
seems to be a nice compromise.  Can I assume that anything truly stunning
in a.a-a that isn't originally cross-posted will eventually make its way
over here for those of us that don't keep up with both?)

-Jay-

-- 
Jay B. Parker -- Mississippi State University -- jbp...@Ra.MsState.Edu
"But I have promises to keep, And miles to go before I sleep."-Frost

In article <2t4vmq$dg...@gagme.wwa.com> jon...@pyrite.cs.uiowa.edu (Douglas W. Jones,201H MLH,3193350740,3193382879) writes:

[...]

>Which, in my eyes, looks pretty good, I think better than your proposed:
>> __   ___   ___
>>  _| |_  |_|  _|
>> |  _  |  _  |_
>> |_| |_| | |___|
>>  _   _  |  ___ 
>> | |_| | |_|  _|
>> |_   _|  _  |_ 
>> __| |___| |___|

>The problem with limiting yourself to | and _ is that the _ hangs over the
>end of each corner, looking a bit sloppy.

... maybe, if you clipped the hang-overs it looks even clearer. Btw: I use 
MS-Windows to read news with the font FixedSys where the dot (.) is a littler 
wider but on the same height as the dot of the exclamation mark (!).



--

                .odbo.
            .od88888888bo.                  Paul Foerster
        .od8888888888888888bo.
    .od888888888888888888888888bo.          pau...@heino.ibh.rwth-aachen.de
 od88888888888888888888888888888888bo
  `~888888888888888888888888888888~'
     `~888888888888888888888888~'|          "Beam me up Scotty, there's no
        `~888888888888888888~'   |              intelligent life down here!"
          |`~888888888888~'|     |
          \   `~888888~'   /     A
           `-_   `~~'   _-'      H
              `--____--'