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Saturday, Dec. 21, 2024

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Complex Numbers

by Waltz Invictus

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

A signature for exclusive use of winners at the 2019 Quill Awards

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

Show Recent Comments

10 Most Recent Blog Comments:

Annette

about 10 hours ago
In response to "Neutral Zone"

It made me happy that I was able to like it. I take the small victories.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

Annette

a day ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

a day ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

Dec 19, 2024 at 9:03pm
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 Like

tj-Merry Mischief Maker

Dec 19, 2024 at 3:43pm
In response to "Five Seconds"

I also ate carrots right out of the garden growing up, I also picked and ate fruits and berries growing in the wild without washing. I do remember food dropped on the floor was either rinsed off and then eaten, or if it was something not easily rinsed, like buttered toast buttered side down, we gave it to the dog.

In our house, there's not a five second rule; unless it's something dogs can't eat, it's whichever one gets it first.

2 Like

🌖 HuntersMoon

Dec 19, 2024 at 8:53am
In response to "Five Seconds"

2 Like

Aiva Raine

Dec 17, 2024 at 7:39pm
In response to "Need for Speed"

Even with the actual explanation- it still left me going- sooooo what's the difference between the special expensive "speed tape" they use for "temporary fixes" and duct tape? LOL- sure sounds like duct tape to me and they are using it for exactly the same reasons you would use duct tape. I'm guessing that the only difference between it and duct tape is the "speed tape" is slightly stronger and handles temperature differences better. It still comes down holding the plane together with tape which doesn't exactly fill me with confidence. Especially if it's a Boeing plane.

1 Like

tj-Merry Mischief Maker

Dec 17, 2024 at 6:14pm
In response to "Need for Speed"

I suppose they call it speed tape to keep people calm. If they called it what it is, temporary repair tape, they may lose passengers.

2 Like

Waltz Invictus

Dec 17, 2024 at 9:43am
In response to "Need for Speed"

Ichabod Crane-- Mince Pie

, I've heard that speed tape is extremely expensive. I can only assume the maintenance guys at Delta got a five-finger discount. But if you're going to steal from work, might as well go big and not just lift a box of paper clips.

1 Like

June 22, 2024 at 8:42am

#1073015

Discomfort Zone

My passport expires in two years. I would like to use it at least once before I get it renewed. Plans I had to travel internationally got interrupted by you-know-what.

Yeah, I'm not doing an article today; I want to talk about this, instead.

The last time I left the country was over 10 years ago; I went to England and stayed with WDC friends there. It didn't require a lot of planning or schedule-keeping on my part, except for, obviously, the flights: no hotel itineraries, no figuring out how to drive on the wrong side of the road, no dining reservations, no navigating a wildly different language (just a moderately different one).

I had a great time, but like I said, I've been languishing in the US (and maybe a little bit in Canada, which hardly counts) since then.

My desire to visit Belgium still stands, though the person I was going to travel with has other priorities now. Which is fine; I'm used to traveling alone and actually enjoy it.

But I've gotten it into my head that, first, I want to go to France. No, not because of the Olympics. Fuck the Olympics and its crowds. If you ask me "what could possibly make Parisians more grumpy," that would be my first answer. Hell, it might even drive them in Seine.

(Not sorry.)

No, it's because un) je comprends un peu de français maintenant, deux) il y a de bon vin là, trois) j'ai entendu que les bières en France sont mieux qu'avant.

(Okay, fine; that's intended to mean "I understand a little French now," "There's good wine there," and "I heard that the beers in France are better than before." Chances are I screwed something up, but at least I tried.)

Of course, there's no reason not to do both countries in one trip, except for that pesky "planning" and "transportation" thing. Unlike the UK, I don't know anyone in France (yet). Or Belgium. And that's mentally blocking me from traveling there alone.

I know that's a "me" thing. Another "me" thing is that I despise flying, especially flying steerage. It's not fear; I've internalized that I'm safer on an airplane than I am sitting on my deck where a tree could fall on me or a mosquito could bite me with a dread disease. No, it's the discomfort, inconvenience, and security theater.

Either of those "me" things by themselves, I can deal with. I've flown across the US, including once to Hawai'i and back. I've also driven across the country (though obviously, not to Hawai'i) solo, without seeing anyone I knew for days at a time. Not to be a dick about it or anything, but I can even ameliorate the coach-class issue by upgrading; since I haven't traveled much in the last four years, my budget for that sort of thing is well-padded.

There are other considerations, too. For example, I know some people travel to get away from it all. I do not. I require guaranteed internet connectivity. Supposedly, my mobile carrier has options for this, but I still don't fully understand them. At a bare minimum, I'd want access to Google Maps. At a slightly less naked minimum, I have a Duolingo streak going that I am loathe to give up. There's also the daily blogging streak that I was hoping I could extend until the end of this year, but as I hate writing on a phone keyboard anyway, that can slip if it needs to (I've already decided I'm not bringing the laptop).

For another example, I'm still a little unclear about how to pay for stuff while out of the country. Even in England, sometimes they had trouble with taking my ass-backwards American credit card, even though it's supposedly specifically tailored for international travel. I imagine that's even worse in the Eurozone. And I don't know how to deal with actual currency exchange. Still, American tourists infest Europe like a disease; obviously, they've found a way to accommodate us. I just don't know what to expect or plan for.

Speaking of which, I also hate being a "tourist." I'd rather be seen as a visitor. Hawaiian shirt and camera notwithstanding.

I shouldn't let these things slow me down, but I do. I'll need to work on that.

On the plus side, I have an electric plug converter that should work in any country civilized enough to have electricity in the first place. You know, for charging up the mobile phone I'm not going to travel without.

In any case, if this happens, it'll be after the goddamn sports thing. I don't necessarily want to visit Paris, but I suspect that crowds everywhere will be worse during that event.

One option I'm considering is, unlike international travel itself, something I've never done: putting it all, or most of it, in the hands of a travel agent.

This appeals to my inherently lazy nature, but I expect it takes a lot of the spontaneity and control out of my hands (yes, I know that "spontaneity" and "control" are basically antonyms, but we've already established that I'm weird). I also have no idea how to go about it, but I'm pretty sure I can figure it out.

I know some readers are seasoned international travelers and might find my hesitation perplexing. But, as I said, I'm just not used to this stuff. My experience with it is limited.

So that's today's blog. I did it mostly to get my own thoughts in order, but advice and comments are always appreciated.

4 Like • Comment • View 11 comments

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