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Friday, Jun. 28, 2024

1:12am EDT

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Complex Numbers

by Robert Waltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

Complex Numbers

A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.

The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.

Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.

Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.

http://www.ddewey.net/mandelbrot/

Signature for Honorable Mentions in 2018 Quill Awards

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Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Adherennium Dr of Phoolishness

about 13 hours ago
In response to "Wave Rider"

Horrifying fact, I once painted a reproduction of the Hokusai wave on our bathroom wall. Eventually of course it was painted over, but I like to fantasise that in some distant future it will be archaeologically excavated and held up as an example of early cultural appropriation, (badly executed too.)

1 Like

Annette

a day ago
In response to "The Oz Hypothesis"

The nekked wimmin look like something that I might have drawn in first grade.

1 Like

Aiva Raine

Jun 25, 2024 at 10:16pm
In response to "Can't Spell Success without Sucs"

Ok- this made me truly LOL- "sipping a gin and tonic made with low-paid laborer tears"

Thank you. Totally agree with the rest of your article.

Money doesn't solve all problems but it sure as hell eliminates many and makes it easier to go places or buy things that can create some happiness. IE- a property somewhere quiet and peaceful and a trailer with which to chill on said property.

Rich people are typically clueless assholes.

1 Like

Anni Pon

Jun 25, 2024 at 9:30am
In response to "Can't Spell Success without Sucs"

I've never heard anyone say, "That guy is so successful, but he doesn't really make much money." Or anything similar. Sure, you can have a positive impact on the world without making lots of money, but people won't call it success.

2 Like

Annette

Jun 23, 2024 at 1:28pm
In response to "Revisited: "Experience""

This is how I coped:

1 Like

Elisa: Middle Aged Stik

Jun 23, 2024 at 9:51am
In response to "Revisited: "Experience""

Not gonna lie I kinda miss Zoom parties, at least for this community since people on WDC are so spread out. Meeting in person is pretty tricky and/or expensive. It's certainly more socializing than I've been doing regularly since, oh, 2022 or so.

As for server migration, well, I work in the IT world. I've been through that. And honestly, server migration is a bit nerve wracking, as some stuff can go missing. It's still more manageable than a complete redesign. Complete redesigns are awful. You can test in different environments that the public can't see till kingdom come, but things always go wrong when the public version is rolled out. A local grocery store recently redid their website, and the old site held thousands of recipes. When the new site was unveiled, none of those recipes made it over. I ended up reaching out on Messenger and was able to get a copy of a recipe I use somewhat often, but I'm kind of annoyed that the text recipes are currently MIA because somehow that data didn't transfer with the site rebuild. Absolute madness.

1 Like

Wordsmitty ✍️

Jun 22, 2024 at 5:56pm
In response to "Discomfort Zone"

Just so everyone is clear:

- There are credit cards and debit cards and even cash cards. They are treated differently by different places as some prefer debit and cash over credit (which usually chrages the merchant more).

- As Annette mentioned, using text and wi-fi is best and usually cheap or free included most US phone plans. However, 'data' outside N. America is not. If you want to wander streets and go hiking and check maps or GPS in Europe, make sure you have a data plan for Europe. That's where the thousands of dollar charges come in if you don't have that. Voice also is usually extra. So if you plan on a lot of talking, get a plan for that, too. (As I recall without an additional plan for Europe, standard charges were 25 or 50 cents for each text and and a dollar minute for voice.)

- On phones, you may have to turn on or unlock the ability to use European system as it communicates differently than the one used in the US. T-Mobile does have good info explanaing that and data plans once you find it on their site. I think there was a search to input your phone make & model to show you what will make it work outside N. America.

1 Like

Elisa: Middle Aged Stik

Jun 22, 2024 at 5:08pm
In response to "Discomfort Zone"

Funny thing is, everyone mentions day to day spending in cash, but I don't recall seeing a single person in the Netherlands use cash in the grocery store. I was in a couple different grocery stores and a convenience store outside normal tourist areas, and cards were preferred. Even in museums there were readers to get donations from cards instead of having boxes out to drop off cash donations. This may be less of a thing in smaller communities, but I do feel like some of the larger (non-tourist) communities are going cash free. The pandemic's legacy of contactless payments sure has been a weird one.

1 Like

Annette

Jun 22, 2024 at 4:51pm
In response to "Discomfort Zone"

I think that SIM card thing is over now. Check it out though. I didn't change my SIM card and I my bill was the exact same as always. I did only use texting and wi-fi though.

1 Like

Robert Waltz

Jun 22, 2024 at 4:46pm
In response to "Discomfort Zone"

Annette

, merci, tu as raison.

I have a pretty recent Samsung phone, and T-Mobile, but I seem to remember something about a different SIM card or activation or something. Easy enough to find out. I know there were horror stories for a while about people traveling and getting hit by surprise roaming fees in the thousands of dollars, so that would be something to avoid.

Thinking about going this autumn, because like you said, it's not summer. Also, hopefully fewer free-range tourist kids. One of the many great things about being me is that I have some flexibility, so I don't yet know exactly when.

1 Like

June 23, 2024 at 9:43am

#1073058

Revisited: "Experience"

We're looking back into November of 2021 today, selected at random as usual. Since the process is random, sometimes there's something of substance, but other times, we get to revisit stuff like this: "Experience"

Which, honestly, suits me just fine because I might be a little bit hung over.

The 30-Day Blogging Challenge was running that month, and the prompt, if you don't want to click on that link, was: "An easy prompt for tonight. I'm tired, don't want to think much, so an easy one. What did you do during the 'Great Shutdown For The Upgrade' of WDC today? Tell us all the 'gory' details!"

I doubt most users even noticed, and doubt even more that, without entries like these, most people remember it now. I've logged in here every day for several years now, but even I can live without it for a few hours.

Hopefully everyone knows we have regular Zoom parties every other week.

Those, of course, no longer happen. Nothing bad; just we all moved on to doing other things. Similar to the 30DBC itself.

All this server migration, website coding, and hosting stuff might as well be sorcery as far as I'm concerned.

Any sufficiently advanced technology, etc., etc.

I think most of us have things like that - specialties that, to other people, seem like magic.

For that matter, being able to write a coherent and compelling story can seem like magic. Hell, these days, it's a miracle if everything in a story, essay, or blog entry gets spelled correctly.

Even with spellcheck.

Besides, I'd rather learn about beer. Preferably through hands-on experience.

Well, last night, it was wine, not beer, but for at least the next few hours, my education is going to have to take a break.

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