[U-Boot-Users] Reading or writing jffs2 - how?

[U-Boot-Users] Reading or writing jffs2 - how?

[Martin Egholm Nielsen]

Hi there,

I have tried to create a jffs2-image of the linux-filesystem I wish to 
use, and then write it to my flash using "nand write.jffs2 100000 0 
$(filesize)". But with no luck...
Then I began to investigate the fundamental "ls" and "nand erase" 
commands, but neither there did I have any success. Below is a trace of 
what I've tried in order to get something working.

In section 2, I'd expect the nand to be mountable from Linux - but's 
it's not.
In section 3, I'd expect the filesystem to be ls'ed correct from u-boot 
- but it's not...

Can someone tell me if there is something I've misunderstood?

********************************
********** 1 U-Boot ************
********************************
U-Boot 1.1.2 (Nov 27 2004 - 11:50:10)
CPU:   IBM PowerPC 405EP Rev. B at 333.333 MHz (PLB=111, OPB=55, EBC=37 MHz)

==== 8< 8< 8< ====

NAND:Probing@0xff400000
   64 MB

==== 8< 8< 8< ====

=> nand erase clean

NAND erase: device 0 offset 0, size 67108864 ... OK

=> ls
Scanning JFFS2 FS:  done.
=>

*******************************
********** 2 Linux ************
*******************************
# cat /proc/mtd

dev:    size   erasesize  name
mtd0: 04000000 00004000 "Trampoline Nand Flash (128 MB)"

# mount -t jffs2 /dev/mtdblock0 mnt/nand0

jffs2: Erase block size too small (16KiB). Using virtual blocks size 
(32KiB) instead
Cowardly refusing to erase blocks on filesystem with no valid JFFS2 nodes
empty_blocks 1325, bad_blocks 4, c->nr_blocks 2048
mount: Mounting /dev/mtdblock0 on /mnt/nand0 failed: Invalid argument

# eraseall /dev/mtd0

Erasingnand_erase: attempt to erase a bad block at p 16 Kibyte @ 400age 
0x00000020
0 --  0 % complenand_erase: attempt to erase te.
eraseall: /a bad block at page 0x00000040
dev/mtd0: MTD Ernand_erase: attempt to erasase failure: Inpe a bad block 
at page 0x00000060
nand_erase: attempt to erase a bad blo
Erasing 16 Kibck at page 0x00000080
yte @ 8000 --  0nand_erase: attempt to er % complete.
erase a bad block at page 0x000000a0
aseall: /dev/mtd0: MTD Erase fainalure: Input/outpnd_erase: attempt to 
erase a b
ad block at page 0x000000c0
ut error
Erasinand_erng 16 Kibyte @ case: attempt to erase a bad block at page 
0x000000e0
000 --  0 % complete.
eraseall: /dev/mtd0: MTD Erase failure: Input/output error
Erasing 16 Kibyte @ 10000 --  0 % complete.
eraseall: /dev/mtd0: MTD Erase failure: Input/output error
Erasing 16 Kibyte @ 14000 --  0 % complete.
eraseall: /dev/mtd0: MTD Erase failure: Input/output error
Erasing 16 Kibyte @ 18000 --  0 % complete.
eraseall: /dev/mtd0: MTD Erase failure: Input/output error
Erasing 16 Kibyte @ 1c000 --  0 % complete.
eraseall: /dev/mtd0: MTD Erase failure: Input/output error
Erased 65536 Kibyte @ 0 -- 100% complete.

# mount -t jffs2 /dev/mtdblock0 /mnt/nand0/

jffs2: Erase block size too small (16KiB). Using virtual blocks size 
(32KiB) instead

# touch /mnt/nand0/testfile
# mkdir /mnt/nand0/testdir
# umount /mnt/nand0

jffs2: No clean, dirty _or_ erasable blocks to GC from! Where are they all?
jffs2: Couldn't find erase block to garbage collect!

# mount -t jffs2 /dev/mtdblock0 /mnt/nand0/

jffs2: Erase block size too small (16KiB). Using virtual blocks size 
(32KiB) instead

# ls -l /mnt/nand0/
drwxr-xr-x    2 0        0               0 Feb  8 05:59 testdir
-rw-r--r--    1 0        0               0 Feb  8 05:59 testfile

********************************
********** 3 U-Boot ************
********************************

=> ls
Scanning JFFS2 FS:  done.
=>


Best regards,
  Martin Egholm

[U-Boot-Users] Reading or writing jffs2 - how?

[Detlev Zundel]

Hi Martin,

> I have tried to create a jffs2-image of the linux-filesystem I wish to
> use, and then write it to my flash using "nand write.jffs2 100000 0
> $(filesize)". But with no luck...
> Then I began to investigate the fundamental "ls" and "nand erase"
> commands, but neither there did I have any success. Below is a trace
> of what I've tried in order to get something working.
>
> In section 2, I'd expect the nand to be mountable from Linux - but's
> it's not.
> In section 3, I'd expect the filesystem to be ls'ed correct from
> u-boot - but it's not...
>
> Can someone tell me if there is something I've misunderstood?
>
> ********************************
> ********** 1 U-Boot ************
> ********************************
> U-Boot 1.1.2 (Nov 27 2004 - 11:50:10)
> CPU:   IBM PowerPC 405EP Rev. B at 333.333 MHz (PLB=111, OPB=55, EBC=37 MHz)
>
> ==== 8< 8< 8< ====
>
> NAND:Probing at 0xff400000
>    64 MB
>
> ==== 8< 8< 8< ====
>
> => nand erase clean
>
> NAND erase: device 0 offset 0, size 67108864 ... OK
>
> => ls
> Scanning JFFS2 FS:  done.
> =>
>
> *******************************
> ********** 2 Linux ************
> *******************************

Which Linux kernel with which mtd code version?

> # cat /proc/mtd
>
> dev:    size   erasesize  name
> mtd0: 04000000 00004000 "Trampoline Nand Flash (128 MB)"
>
> # mount -t jffs2 /dev/mtdblock0 mnt/nand0
>
> jffs2: Erase block size too small (16KiB). Using virtual blocks size
> (32KiB) instead
> Cowardly refusing to erase blocks on filesystem with no valid JFFS2 nodes
> empty_blocks 1325, bad_blocks 4, c->nr_blocks 2048
> mount: Mounting /dev/mtdblock0 on /mnt/nand0 failed: Invalid argument
>
> # eraseall /dev/mtd0

Use -j (--jffs2) in the future.

> Erasingnand_erase: attempt to erase a bad block at p 16 Kibyte @
> 400age 0x00000020
> 0 --  0 % complenand_erase: attempt to erase te.
> eraseall: /a bad block at page 0x00000040
> dev/mtd0: MTD Ernand_erase: attempt to erasase failure: Inpe a bad
> block at page 0x00000060
> nand_erase: attempt to erase a bad blo
> Erasing 16 Kibck at page 0x00000080
> yte @ 8000 --  0nand_erase: attempt to er % complete.
> erase a bad block at page 0x000000a0
> aseall: /dev/mtd0: MTD Erase fainalure: Input/outpnd_erase: attempt to
> erase a b
> ad block at page 0x000000c0
> ut error
> Erasinand_erng 16 Kibyte @ case: attempt to erase a bad block at page
> 0x000000e0
> 000 --  0 % complete.
> eraseall: /dev/mtd0: MTD Erase failure: Input/output error
> Erasing 16 Kibyte @ 10000 --  0 % complete.
> eraseall: /dev/mtd0: MTD Erase failure: Input/output error
> Erasing 16 Kibyte @ 14000 --  0 % complete.
> eraseall: /dev/mtd0: MTD Erase failure: Input/output error
> Erasing 16 Kibyte @ 18000 --  0 % complete.
> eraseall: /dev/mtd0: MTD Erase failure: Input/output error
> Erasing 16 Kibyte @ 1c000 --  0 % complete.
> eraseall: /dev/mtd0: MTD Erase failure: Input/output error
> Erased 65536 Kibyte @ 0 -- 100% complete.

Might be caused be eraseall without -j ignoring bad blocks but I'm not
sure.

> # mount -t jffs2 /dev/mtdblock0 /mnt/nand0/
>
> jffs2: Erase block size too small (16KiB). Using virtual blocks size
> (32KiB) instead
>
> # touch /mnt/nand0/testfile
> # mkdir /mnt/nand0/testdir
> # umount /mnt/nand0
>
> jffs2: No clean, dirty _or_ erasable blocks to GC from! Where are they all?
> jffs2: Couldn't find erase block to garbage collect!

Thats just a warning and can be ignored - iirc it means the unmount
triggered a garbage collection which found nothing to collect.

> # mount -t jffs2 /dev/mtdblock0 /mnt/nand0/
>
> jffs2: Erase block size too small (16KiB). Using virtual blocks size
> (32KiB) instead
>
> # ls -l /mnt/nand0/
> drwxr-xr-x    2 0        0               0 Feb  8 05:59 testdir
> -rw-r--r--    1 0        0               0 Feb  8 05:59 testfile
>
> ********************************
> ********** 3 U-Boot ************
> ********************************
>
> => ls
> Scanning JFFS2 FS:  done.
> =>

This should definitely work (it worked for me on 8xx and 4xx in the
past).

Check the mtd code in your Linux version - many improvements related
to NAND went in there not long ago.

Cheers
  Detlev

-- 
In God we trust.  All others we monitor
                       -- NSA motto

[U-Boot-Users] Reading or writing jffs2 - how?

[Detlev Zundel]

Hi Martin,

> I have tried to create a jffs2-image of the linux-filesystem I wish to
> use, and then write it to my flash using "nand write.jffs2 100000 0
> $(filesize)". But with no luck...
> Then I began to investigate the fundamental "ls" and "nand erase"
> commands, but neither there did I have any success. Below is a trace
> of what I've tried in order to get something working.

Are you really sure, your NAND gets accessed correctly both under
U-Boot and Linux?  Can you erase / write / readback some data under
U-Boot by hand?

Cheers
  Detlev

-- 
The only use I can find for vi is editing the emacs sources while
porting them to a new machine.
                                        -- Larry Campbell

[U-Boot-Users] Re: Reading or writing jffs2 - how?

[Martin Egholm Nielsen]

Hi Detlev,

>>I have tried to create a jffs2-image of the linux-filesystem I wish to
>>use, and then write it to my flash using "nand write.jffs2 100000 0
>>$(filesize)". But with no luck...
>>Then I began to investigate the fundamental "ls" and "nand erase"
>>commands, but neither there did I have any success. Below is a trace
>>of what I've tried in order to get something working.
> Are you really sure, your NAND gets accessed correctly both under
> U-Boot and Linux?  Can you erase / write / readback some data under
> U-Boot by hand?
I'm sure it works under Linux - there I can both write and read - boot 
and use the flash-data again. No problems.

Under u-boot I've just tried the following:

=============== 8< 8< 8< 8< ===============

=> md.b 100000

00100000: 7f a3 eb 78 38 a0 00 00 4b ff fa b1 7c 7f 1b 78 
...x8...K...|..x
00100010: 3d 40 c0 18 39 2a 14 60 81 69 00 08 39 6b ff ff 
=@..9*.`.i..9k..
00100020: 91 69 00 08 2c 0b 00 00 40 82 00 10 80 0a 14 60 
.i..,... at ......`
00100030: 2c 00 00 00 40 82 00 0c 7f e3 fb 78 4b ff fe a0 
,... at ......xK...

=> nand write 100000 0 40

NAND write: device 0 offset 0, size 64 ... Warning block writes should 
be at lea
st 512 bytes and start on a 512 byte boundry
  64 bytes written: OK

=> nand read 200000 0 40

NAND read: device 0 offset 0, size 64 ... Warning block writes should be 
at leas
t 512 bytes and start on a 512 byte boundry
  64 bytes read: OK

=> md.b 200000

00200000: 7f a3 eb 78 38 a0 00 00 4b ff fa b1 7c 7f 1b 78 
...x8...K...|..x
00200010: 3d 40 c0 18 39 2a 14 60 81 69 00 08 39 6b ff ff 
=@..9*.`.i..9k..
00200020: 91 69 00 08 2c 0b 00 00 40 82 00 10 80 0a 14 60 
.i..,... at ......`
00200030: 2c 00 00 00 40 82 00 0c 7f e3 fb 78 4b ff fe a0 
,... at ......xK...

=>

=============== 8< 8< 8< 8< ===============

In short: the giberish-data present at memory 0x100000 is written to 
flash, and reread again to memory at 0x200000. The flash does still 
contain the data after reboot.

Next, I tried reading the data from my Linux:

# dd if=/dev/mtd0 of=/ftp/dump bs=8 count=8

=== /ftp/dump contains: ===

00000000: 7fa3 eb78 38a0 0000 4bff fab1 7c7f 1b78  ...x8...K...|..x
00000010: 3d40 c018 392a 1460 8169 0008 396b ffff  =@..9*.`.i..9k..
00000020: 9169 0008 2c0b 0000 4082 0010 800a 1460  .i..,... at ......`
00000030: 2c00 0000 4082 000c 7fe3 fb78 4bff fea0  ,... at ......xK...

Hence, the same data is available from Linux at the beginning at the device.

That made me wonder... Aaaaand, then I tried mounting the 
flash-root-filesystem under Linux after what I thought would have 
corrupted it (the above writing of giberish to the system). And the 
root-filesystem still worked!
Hence, I tried dumping the entire flash to a file. And I discovered that 
the filesystem-data was positioned@the "end" of the flash...
That may be the reason that "ls" in u-boot does not work with the image 
in flash - or what?

Best regards,
  Martin Egholm

[U-Boot-Users] Re: Reading or writing jffs2 - how?

[Martin Egholm Nielsen]

Hi Detlev,

>> I have tried to create a jffs2-image of the linux-filesystem I wish
>> to use, and then write it to my flash using "nand write.jffs2
>> 100000 0 $(filesize)". But with no luck... Then I began to
>> investigate the fundamental "ls" and "nand erase" commands, but
>> neither there did I have any success. Below is a trace of what I've
>> tried in order to get something working.
> Are you really sure, your NAND gets accessed correctly both under 
> U-Boot and Linux?  Can you erase / write / readback some data under 
> U-Boot by hand?
I'm sure it works under Linux - there I can both write and read - boot
and use the flash-data again. No problems.

Under u-boot I've just tried the following:

=============== 8< 8< 8< 8< ===============

=> md.b 100000

00100000: 7f a3 eb 78 38 a0 00 00 4b ff fa b1 7c 7f 1b 78
...x8...K...|..x
00100010: 3d 40 c0 18 39 2a 14 60 81 69 00 08 39 6b ff ff
=@..9*.`.i..9k..
00100020: 91 69 00 08 2c 0b 00 00 40 82 00 10 80 0a 14 60
.i..,... at ......`
00100030: 2c 00 00 00 40 82 00 0c 7f e3 fb 78 4b ff fe a0
,... at ......xK...

=> nand write 100000 0 40

NAND write: device 0 offset 0, size 64 ... Warning block writes should
be at lea
st 512 bytes and start on a 512 byte boundry
  64 bytes written: OK

=> nand read 200000 0 40

NAND read: device 0 offset 0, size 64 ... Warning block writes should be
at leas
t 512 bytes and start on a 512 byte boundry
  64 bytes read: OK

=> md.b 200000

00200000: 7f a3 eb 78 38 a0 00 00 4b ff fa b1 7c 7f 1b 78
...x8...K...|..x
00200010: 3d 40 c0 18 39 2a 14 60 81 69 00 08 39 6b ff ff
=@..9*.`.i..9k..
00200020: 91 69 00 08 2c 0b 00 00 40 82 00 10 80 0a 14 60
.i..,... at ......`
00200030: 2c 00 00 00 40 82 00 0c 7f e3 fb 78 4b ff fe a0
,... at ......xK...

=>

=============== 8< 8< 8< 8< ===============

In short: the giberish-data present at memory 0x100000 is written to
flash, and reread again to memory at 0x200000. The flash does still
contain the data after reboot.

Next, I tried reading the data from my Linux:

# dd if=/dev/mtd0 of=/ftp/dump bs=8 count=8

=== /ftp/dump contains: ===

00000000: 7fa3 eb78 38a0 0000 4bff fab1 7c7f 1b78  ...x8...K...|..x
00000010: 3d40 c018 392a 1460 8169 0008 396b ffff  =@..9*.`.i..9k..
00000020: 9169 0008 2c0b 0000 4082 0010 800a 1460  .i..,... at ......`
00000030: 2c00 0000 4082 000c 7fe3 fb78 4bff fea0  ,... at ......xK...

Hence, the same data is available from Linux at the beginning at the device.

That made me wonder... Aaaaand, then I tried mounting the
flash-root-filesystem under Linux after what I thought would have
corrupted it (the above writing of giberish to the system). And the
root-filesystem still worked!
Hence, I tried dumping the entire flash to a file. And I discovered that
the filesystem-data was positioned@the "end" of the flash...
That may be the reason that "ls" in u-boot does not work with the image
in flash - or what?

Best regards,
  Martin Egholm

[U-Boot-Users] Re: Reading or writing jffs2 - how?

[Martin Egholm Nielsen]

Hi Detlev,

>>I have tried to create a jffs2-image of the linux-filesystem I wish to
>>use, and then write it to my flash using "nand write.jffs2 100000 0
>>$(filesize)". But with no luck...
>>Then I began to investigate the fundamental "ls" and "nand erase"
>>commands, but neither there did I have any success. Below is a trace
>>of what I've tried in order to get something working.
> Are you really sure, your NAND gets accessed correctly both under
> U-Boot and Linux?  Can you erase / write / readback some data under
> U-Boot by hand?
The problem has been solved...
The reason that "ls" didn't work from u-boot, was that the boards' 
u-boot config-file included an erroneous nand-size:

#define CONFIG_JFFS2_NAND_SIZE 64*1024*1024

My board had only one configuration-file associated, but multiple 
nand-size configurations.

The jffs2-image problems were related to the endianess problems of 
mkfs.jffs2:

http://lists.infradead.org/pipermail/linux-mtd/2004-January/009091.html

Thanks for all,
  Martin

[U-Boot-Users] Re: Reading or writing jffs2 - how?

[Detlev Zundel]

Hi Martin,

> The problem has been solved...
> The reason that "ls" didn't work from u-boot, was that the boards'
> u-boot config-file included an erroneous nand-size:
>
> #define CONFIG_JFFS2_NAND_SIZE 64*1024*1024

Yes, I was about to check the options available in U-Boot and ask you
to verify those but you beat me to it.

> My board had only one configuration-file associated, but multiple
> nand-size configurations.
>
> The jffs2-image problems were related to the endianess problems of
> mkfs.jffs2:
>
> http://lists.infradead.org/pipermail/linux-mtd/2004-January/009091.html

Another reason for using our ELDK - it has a working mkfs.jff2 ;)

Cheers
  Detlev

-- 
He who can properly define and divide is to be considered a god.
                                        -- Plato

[U-Boot-Users] Re: Reading or writing jffs2 - how?

[Martin Egholm Nielsen]

Hi Detlev,

>>The problem has been solved...
>>The reason that "ls" didn't work from u-boot, was that the boards'
>>u-boot config-file included an erroneous nand-size:
>>#define CONFIG_JFFS2_NAND_SIZE 64*1024*1024
> Yes, I was about to check the options available in U-Boot and ask you
> to verify those but you beat me to it.
:-)

>>My board had only one configuration-file associated, but multiple
>>nand-size configurations.
>>The jffs2-image problems were related to the endianess problems of
>>mkfs.jffs2:
>>http://lists.infradead.org/pipermail/linux-mtd/2004-January/009091.html
> Another reason for using our ELDK - it has a working mkfs.jff2 ;)
Noo?! I used mkfs.jffs2 from ELDK 3.0:

# mkfs.jffs2 --version
mkfs.jffs2 revision 1.25

# which mkfs.jffs2
/usr/local/eldk/usr/bin/mkfs.jffs2

# cat /usr/local/eldk/version
ELDK version 3.0
ppc_4xx: Build 2004-02-16

But ofcourse, I guess the above error blocked u-boot from putting the 
correct image in the nand...

BR,
  Martin Egholm

[U-Boot-Users] Re: Reading or writing jffs2 - how?

[Wolfgang Denk]

Dear Martin,

in message <41C7E65C.7030002@egholm-nielsen.dk> you wrote:
> 
> > Another reason for using our ELDK - it has a working mkfs.jff2 ;)
> Noo?! I used mkfs.jffs2 from ELDK 3.0:

Of course Detlev means: use the latest  and  greates  ELDK  -  i.  e.
release 3.1

> # mkfs.jffs2 --version
> mkfs.jffs2 revision 1.25

-> mkfs.jffs2 --version
mkfs.jffs2: revision 1.42

> # cat /usr/local/eldk/version
> ELDK version 3.0
> ppc_4xx: Build 2004-02-16

That's too old:

---------------------
PatchSet 342 
Date: 2004/06/16 11:57:35
Author: wd
Branch: HEAD
Tag: (none)  
Log:
Use mtd-snapshot-20040608 to get a more recent version of
mkfs.jffs2 as needed for NAND flash support.
   
Members: 
        cpkgs.lst:1.42->1.43 
        tarballs.lst:1.37->1.38 
        cross_rpms/mtd_utils/SOURCES/mtd_utils-jffs2.patch:1.1->1.2 
        cross_rpms/mtd_utils/SPECS/mtd_utils.spec:1.1->1.2 
   
---------------------

> But ofcourse, I guess the above error blocked u-boot from putting the 
> correct image in the nand...

Indeed.

Best regards,

Wolfgang Denk

-- 
Software Engineering:  Embedded and Realtime Systems,  Embedded Linux
Phone: (+49)-8142-66989-10 Fax: (+49)-8142-66989-80 Email: wd at denx.de
"I like your game but we have to change the rules."

[U-Boot-Users] Re: Reading or writing jffs2 - how?

[Martin Egholm Nielsen]

Hi Wolfgang,

>>>Another reason for using our ELDK - it has a working mkfs.jff2 ;)
>>Noo?! I used mkfs.jffs2 from ELDK 3.0:
> Of course Detlev means: use the latest  and  greates  ELDK  -  i.  e.
> release 3.1
But of course he does :-)
Cannot connect to ftp://ftp.leo.org/, though. Connection refused...

I'll try fetching it - then everybody's going to get happy...

Thanks,
  Martin

[U-Boot-Users] Re: Reading or writing jffs2 - how?

[Wolfgang Denk]

In message <41C7ED34.9020208@egholm-nielsen.dk> you wrote:
> 
> > Of course Detlev means: use the latest  and  greates  ELDK  -  i.  e.
> > release 3.1
> But of course he does :-)
> Cannot connect to ftp://ftp.leo.org/, though. Connection refused...

Yes, LEO's FTP server has been broken for sevcaral months now.

HTTP access works, though. And there are other mirrors: see
http://www.denx.de/twiki/bin/view/DULG/ELDKAvailability

> I'll try fetching it - then everybody's going to get happy...

:-)

Best regards,

Wolfgang Denk

-- 
Software Engineering:  Embedded and Realtime Systems,  Embedded Linux
Phone: (+49)-8142-66989-10 Fax: (+49)-8142-66989-80 Email: wd at denx.de
The perversity of nature is nowhere better demonstrated by  the  fact
that,  when  exposed to the same atmosphere, bread becomes hard while
crackers become soft.

[U-Boot-Users] Re: Reading or writing jffs2 - how?

[Martin Egholm Nielsen]

>>But of course he does :-)
>>Cannot connect to ftp://ftp.leo.org/, though. Connection refused...
> Yes, LEO's FTP server has been broken for sevcaral months now.
Ohh... Someone should update the wiki-doc:
http://www.denx.de/twiki/bin/view/DULG/ELDKDownloadPowerPC

Super!
  Martin

[U-Boot-Users] Re: Reading or writing jffs2 - how?

[Detlev Zundel]

Hi Martin,

>>>My board had only one configuration-file associated, but multiple
>>>nand-size configurations.
>>>The jffs2-image problems were related to the endianess problems of
>>>mkfs.jffs2:
>>>http://lists.infradead.org/pipermail/linux-mtd/2004-January/009091.html
>> Another reason for using our ELDK - it has a working mkfs.jff2 ;)
> Noo?! I used mkfs.jffs2 from ELDK 3.0:
>
> # mkfs.jffs2 --version
> mkfs.jffs2 revision 1.25
>
> # which mkfs.jffs2
> /usr/local/eldk/usr/bin/mkfs.jffs2
>
> # cat /usr/local/eldk/version
> ELDK version 3.0
> ppc_4xx: Build 2004-02-16
>
> But ofcourse, I guess the above error blocked u-boot from putting the
> correct image in the nand...

Yes, I think that failure cannot be attributed to an endianness
problem in the mkfs.jffs in the ELDK which works.

Cheers
  Detlev

-- 
Progress in  mathematics comes from  repeated acts of generalization.
If mathematics is anything, it is the art of chosing the most elegant
generalization for some abstract pattern.  Thus esthetics is central.
                                     -- Douglas Hofstadter