DM42 OFF Images

[jgoizueta]

Here are some images suitable for use n the DM42 OFFIMG directory.

  hp42s_1.bmp (Size: 12.31 KB / Downloads: 446)
  hp42s_2.bmp (Size: 12.31 KB / Downloads: 361)
  hp42s_3.bmp (Size: 12.31 KB / Downloads: 331)

[jgoizueta]

A few more here:

  sliderule_1.bmp (Size: 12.31 KB / Downloads: 407)
  sliderule_2.bmp (Size: 12.31 KB / Downloads: 299)
  sliderule_3.bmp (Size: 12.31 KB / Downloads: 276)

[Geoff Quickfall]

I like the slide ruler.

Of course you can load all three images and watch the off screen cycle them.

Post these at the DM 42S swissmicros form.

Thanks

[Eddie W. Shore]

Nice, classic images. Thanks for posting.

Eddie

[anetzer]

One of my all time favourites. I hope you like it...

[xollins]

Here are 3 I thought I'd share:

  hp_logo1b.bmp (Size: 12.31 KB / Downloads: 235)

  escherb.bmp (Size: 12.31 KB / Downloads: 218)

  hp_logo2b.bmp (Size: 12.31 KB / Downloads: 218)

[Joe Horn]

Want your DM42's powered-off screen to display some famous irrational numbers? The most information-dense way to do this is to use every pixel to represent one binary digit of the irrational number. That way you'll see the most significant 96 thousand bits (roughly as accurate as 28,898 decimal digits).

Here are eleven such "Off Images" for your DM42 in one zipfile. I had HOPED that they would look at least slightly different from each other, but to my eye they all look like utterly random noise. But they are all accurate to the last bit (thanks to the Spigot program). The "decimal point" was ignored when making these, since where it belongs is obvious (can you tell that I grew up using slide rules?).

Zipped collection of all 11 images: https://holyjoe.net/images/DM42/BinaryOffImg.zip

Sneak preview of the images:

[LinusSch]

(06-10-2022 06:50 AM)Joe Horn Wrote:  I had HOPED that they would look at least slightly different from each other, but to my eye they all look like utterly random noise.

This is a great concept, however, all irrational numbers should look like utterly random noise when inspected like this. With rational numbers there should be patterns. So let me suggest a slight tweak: create these images for increasingly accurate rational approximations of pi, ending with the exact one already created, for a set of images with hopefully interesting differences!

[Joe Horn]

(06-10-2022 07:16 AM)LinusSch Wrote:  

(06-10-2022 06:50 AM)Joe Horn Wrote:  I had HOPED that they would look at least slightly different from each other, but to my eye they all look like utterly random noise.

This is a great concept, however, all irrational numbers should look like utterly random noise when inspected like this. With rational numbers there should be patterns.

I hope I'm not being pedantic by disagreeing. Rational numbers *can* have patterns in their decimal (or any other base) expansion. They just can't have *repeating* patterns. The example usually given is 1.010010001000010000010000001... where each string of zeros contains one more zero than the previous string. That's a definite pattern, but it never repeats, so the overall number is irrational. Furthermore, the word "repeating" must be clarified, since repeated strings of 3 zeros between all the digits of pi (3.00010004000100050009...) has a "repeated pattern" of 3 zeros, but they're interrupted by the digits of pi, so the overall number again is irrational.

Therefore, images whose pixels represent the bits of a binary irrational number *can* contain eye-catching patterns. The 11 values I chose above just didn't happen to do that.

(06-10-2022 07:16 AM)LinusSch Wrote:  So let me suggest a slight tweak: create these images for increasingly accurate rational approximations of pi, ending with the exact one already created, for a set of images with hopefully interesting differences!

Intriguing! It will be far easier to get patterns this way, since the partial quotients of many irrational numbers *do* follow patterns, e.g. the constant e whose continued fraction expansion is {2;1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12...} and the continued fraction for tan(1 radian) is {1;1,1,3,1,5,1,7,1,9,1,11...} which are not *repeating* patterns, but they are definitely recognizable and extendable patterns. So the task at hand is to find ones whose pattern looks good in binary. Thanks for the delightful challenge!

[Joe Horn]

Here's an example of an irrational number which does not look like random noise when converted from binary into on/off pixels:

The first 96000 bits of the irrational binary number 010011000111000011110000011111...

[rprosperi]

Cool!

This clearly says something, but I'm not sure what...

[StephenG1CMZ]

(06-02-2020 10:03 AM)jgoizueta Wrote:  A few more here:

Seeing those sliderules onscreen, made me think it would be really cool if a modern calculator could draw an animated sliderule showing it performing the calculation being performed.

[EdS2]

(06-10-2022 06:50 AM)Joe Horn Wrote:  Want your DM42's powered-off screen to display some famous irrational numbers?

Yes! (Although I don't have a DM42...) But rather than the information-dense binary form, I thought I'd have a go with the continued fraction form... see the zip file.

Here's a kind of preview, I hope:
   

For a discussion of the technique, or the idea, please see my specific thread:

(06-13-2022 07:32 PM)EdS2 Wrote:  This might not be new to the world, but it's new to me...

A new way to view continued fractions

[BruceH]

(06-11-2022 11:52 AM)rprosperi Wrote:  This clearly says something, but I'm not sure what...

It says: the answer you're looking for lies somewhere near the rings of Saturn.

[johanw]

(06-11-2022 12:12 PM)StephenG1CMZ Wrote:  Seeing those sliderules onscreen, made me think it would be really cool if a modern calculator could draw an animated sliderule showing it performing the calculation being performed.

It could be a nice instruction manual for people like me who just missed the slide rule era and don't know how to use one (I never found the time to start learning it).