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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:

tj-Merry Mischief Maker

about 13 hours 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

about 18 hours ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

about 18 hours ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

a day ago
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

a day ago
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

a day ago
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

Ichabod Crane-- Mince Pie

Dec 17, 2024 at 9:06am
In response to "Need for Speed"

One of the last jobs I had was with Delta. I did ask the maintanace guys about that tape once and they pointed out high speed will rip duct tape or any other tape right off. They used it personally for their boats sometimes because of its strength. But looking out a window at 400 miles an hour and 30 thousand feet up and see duct tape on the wing. Certainly made me nervous first time I saw it.

3 Like

September 5, 2024 at 9:04am

#1076299

Writing It Off

"Blog Week Birthday Bastion 2024"

[13+] by WakeUpAndLive~"HoHoHo"

Prompt 5. Sept 5.

The more that you read, the more things you will know. The more that you learn, the more places you'll go. Dr. Seuss
Tell us more about the writer in you. Plans/Aspirations/Fears/Status etc?

Plans: None. As a writer, anyway. Apart from continuing to do what I'm doing now. Other than writing, I plan to travel more. I may write about it, but the travel writing field is crowded with young influenzas who can't write for shit, but look good in selfies.

Aspirations: None. Used to be, I wanted to get published. I abandoned that goal, I don't know, maybe about when I turned 50? No one wants to publish old, unestablished writers. Well, almost no one. You can probably find a counterexample if you look for one, because it made the news. It made the news for the same reason lottery wins and lightning strikes do: it's rare. Plus, I'd have to be an exceptional writer. I may be a decent writer, but I'm not exceptional in any way.

And don't say "self-publishing" at me. While it's absolutely a legitimate route, it involves way more work than I'm willing to do, including marketing. I hate marketing, not to mention it would be hypocritical of me to push ads on people while hating all the ads being pushed on me.

Not that I'm above being hypocritical, of course. That just seems a step too far.

Fears: Tornadoes, picking up dog shit, anything touching my eyeballs, and success.

The tornado thing is probably understandable. Not that I live in an especially twister-prone area; it's just that they are, to me, natural disasters worse than earthquakes, floods, fires, or volcanoes.

Picking up dog shit is just something that grosses me out. Thus, I don't have a dog. Every once in a while I'll owe a favor to someone, and sometimes that favor means walking their dog while they're on vacation. Just because I can work through my fears doesn't mean I want to. (Before you ask, cat shit doesn't bother me as much, though it's still not my favorite chore to clean up.)

I also dealt with the eyeball thing a few years ago, because I had to. That doesn't mean I'm eager to have eye surgery again.

The "success" one does relate to writing. Let's say a miracle happens and I get one of my novels published. Suddenly, I'm expected to write more. You know what happens to me when I'm expected to do something? It becomes work, and I'm violently allergic to work.

Status: Another English word with more than one meaning. From context, I'm guessing this is the "how are things going" definition, as in "status report." Answer: cruising along. As for the other definition, where I fit in the social hierarchy, well, I reject the concept of a social hierarchy. But that's really irrelevant; I just like to play with words.

In any case, there is one writing-related thing that's been on my mind lately. As I've mentioned a few times, I've done a blog entry every day for nearly 5 years. Whether it's prompted like this one, or a spontaneous personal update, or commenting on some article, I've managed to find something to say every day since December 14, 2019. This wasn't planned; I just blogged every day for a few months, and the plan after that was to go to Scotland for a couple of weeks for the Islay Festival. Then, well, you know what happened in early 2020. I didn't go anywhere. I kept blogging. When I finally was able to go somewhere, I stayed in the US, and still managed to get an entry in every day.

This will end.

It may end during my upcoming Europe trip, now only 2 weeks away. That's not the plan, but it could happen. My shit gets stolen or broken, or I can't connect to the internet, or I just get too busy and/or too drunk, or I fuck up the time zone difference. I don't know.

Ideally, though, I continue on this track until at least December 13, completing a 5-year daily blogging streak. That's as close to a "plan" as I get with writing, these days.

In either case, though, blogs here are limited to 3000 entries, and this is entry number 2812. Less than 200 to go. Enough to take me to early next year if I continue at this rate, but then... bam! Brick wall.

Other people here have dealt with the limit by deleting old entries. I won't do that. Most never have to worry about the limit, and that's perfectly okay. But I've been considering what to do next. Quit? Start a new blog? Concentrate on fiction and poetry for a while? If I started a new blog, I'd have to think of a title that's somehow works as well as, or better than, Complex Numbers, and on that front, I'm stumped.

Oh well, at least it wouldn't be work.

Heading into the last days of Birthday week, now. We get to give out a free Merit Badge every day this week. Want one? Anyone who comments here before 11:30 pm WDC time today could get today's. (I'll need that extra half-hour to pick a winner and send the badge before midnight.)

To clarify:

When I say "comment," I mean comment. Not review. Though reviews are always welcome.

I also mean "here," not on the newsfeed post.

MB recipient will be chosen at random.

Maximum of one MB per commenter for the week.

If I don't get comments, I'll pick a previous commenter, and maybe not at random.

The MB will be the one I commissioned two years ago, "Complexity," which is a publicly available MB.

I appreciate all comments; this is just a little incentive.

4 Like • Comment • View 12 comments

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