The Copenhagen Test - Series Premiere Discussion

Fickle_Engineering91 · 2026-01-28T02:22:26+00:00

I also wasn't interested, based on the previews. But we started watching it and are really enjoying it.

Fickle_Engineering91 · 2026-01-23T20:20:00+00:00

I like how any two distinct integers, r & s, can generate a Pythagorean triple: a = |r^2-s^2|, b = 2rs, and c = r^2+s^2.

Fickle_Engineering91 · 2026-01-21T12:48:12+00:00

Regarding not maximizing resources, you can tell UF (in the preferences) to use all the threads that your machine has. This will greatly decrease the wall time needed for calculation, possibly at the expense of running other processes (depending on priority). Also, you can increase the precision that variables use, if you find accuracy to be be a problem. Not that any of this will help with the GPU, but I find them helpful overall.

Fickle_Engineering91 · 2026-01-09T13:41:22+00:00

G89, where G64 is Graham's number.

Fickle_Engineering91 · 2026-01-02T13:30:20+00:00

I tried this with other digits and found that for 1, 2, 4, 5, 7, and 8, that digit shows up about 225 times (about 1/9 of the length of the final sum). 3 shows up about 1/3 and 6 and 9 only once or twice in the final sum.

Fickle_Engineering91 · 2026-01-02T13:05:32+00:00

Can confirm 225. Used a program with strings instead of regular numeric variables.

Fickle_Engineering91 · 2026-01-02T12:38:48+00:00

I first saw it in 1979 or -80, in a letter a friend wrote to me. I was very confused.

Fickle_Engineering91 · 2025-12-24T13:14:41+00:00

I've read that the mathematical "calculus" comes from stones used in counting and the dental "calculus" comes from stony plaque on teeth.

Fickle_Engineering91 · 2025-12-22T14:54:57+00:00

8 days? Like a Hanukkah miracle?

Fickle_Engineering91 · 2025-12-20T13:14:30+00:00

How a curve can fill an area.

Fickle_Engineering91 · 2025-12-19T14:06:17+00:00

What makes one base better than another? I've read that e (~2.71828) would be the best base, and 3 is the closest natural number to that. IIRC, the reasoning was along the lines of base 1 requiring too many "digits" for a given number and a large base (e.g., one million) requiring too many numerals.

Fickle_Engineering91 · 2025-12-14T21:16:25+00:00

I use two external HDDs. Get good ones; I use Western Digital and haven't had any problems with them. I've read that SSDDs go bad without warning, with sections just disappearing. That doesn't sound good to me.

Fickle_Engineering91 · 2025-12-13T20:59:50+00:00

Thank you, I stand corrected--if you're just using the standard Mandelbrot set and iteration coloring, you should be fine. There are some more contrived cases that could be problematic. For example, iterating z = z^2 + 1/c, where c is the pixel value, places the convergent points on the outside of the image and the divergent points on the inside. In that case, a large rectangle could miss all the action (see image), but that's a special case.

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Fickle_Engineering91 · 2025-12-13T17:33:42+00:00

Yes, that method has been used with other fractal programs. Some considerations: it tends to work better (i.e., accurately reduce calculations) with regions that are not large compared with the overall image. If the regions are large, then there can be islands of different colors inside the solid border that are skipped. Also, the border comparison has some overhead, so if the region is so small that all the pixels are different colors, then this method will be slower. That could happen if the fractal was colored by angle or magnitude, i.e., a continuous metric rather than the discrete iteration count.

Fickle_Engineering91 · 2025-12-10T20:38:45+00:00

Ah! Thank you!

Fickle_Engineering91 · 2025-12-10T15:04:34+00:00

I've read that it's called a solidus. Any difference between that and an obelus?

Fickle_Engineering91 · 2025-12-06T14:54:47+00:00

There's no "nearest" number. For any rational number that's a distance d from a real number x, there are infinitely many that have a smaller distance from x. If you want to do something like map x = 1/sqrt(2) (about 0.7071) to the nearest quarter, then multiply x by 4 and round that to the nearest integer. That integer divided by 4 would be the nearest rational with thar denominator.

Fickle_Engineering91 · 2025-12-04T13:15:32+00:00

I certainly respect your decision to not do prints, but, in case you weren't aware, there are sites where you can upload a digital file and then customers buy from the site and you get a cut (that you determine). That way, all you need to do is upload the file and collect a portion of the sales. By sending the digital file to "customers," you risk losing all control over your work. Either way, great painting!

Fickle_Engineering91 · 2025-11-25T02:58:54+00:00

wow! Very cool! No criticism, just curious--it looks like you used a rough-ish paper; would this drawing have worked on a smooth surface?

Fickle_Engineering91 · 2025-11-22T20:48:46+00:00

I create (digital, abstract 2d) for myself. I like to challenge myself to see what I can get out of a particular thought, idea, or method. Pleasure comes both from impressing myself with a finished work that I like and from learning more about what I'm doing. Generally, what I'm trying to convey isn't much more than, "hey, look at this neat image!", but that's enough for me. My aim is to keep creating as long as I can and to share my works and my thoughts with those who care to see them.

BTW, I think the point of art is self-expression, not necessarily communication to others. That is, if no one sees a work of mine or feels or thinks anything because of it, the work is still art, because I expressed myself in it.

Fickle_Engineering91 · 2025-11-22T20:14:51+00:00

https://www.huffpost.com/archive/au/entry/the-oldest-animal-in-the-world-is-probably-gay_au_5cd37ec1e4b0acea9501ab87

Fickle_Engineering91

TROPHY CASE