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Sunday, Dec. 22, 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 18 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

September 7, 2024 at 7:20am

#1076413

Spit in the Ocean

"Blog Week Birthday Bastion 2024"

[13+] by WakeUpAndLive~"HoHoHo"

Prompt 7. Sept 7.

The world is not an ideal place for lots of people. What can YOU do to make it better?

Well, the one most overwhelmingly important thing I have already done is: avoid bringing another human into a far-from-ideal world.

The second most important thing is that I attempt to bring knowledge and comedy into an ignorant and largely humorless world. In that, I fail most of the time, but at least it makes me feel good to try.

And there are other things I do. I recycle, to the extent that I'm able. I help out with causes, when I can be sure that it's going more to the cause than to the organizer. I try to minimize my water use, and refrain from littering. All of that amounts to spit in the ocean, and it doesn't even make me feel good to brag about it. And for every infinitesimal improvement we can make individually, millions of times worse stuff gets done by other people, governments, and big corporations. "Every little bit helps," my ass. You think it makes a difference if you give a dollar to a billionaire? No, they only notice if you try to take one.

If there's anything that the pandemic years drove home to me, it's that any effort we make has to be a collective effort—and that it will never be a collective effort. There will always be those who deliberately make things worse. If an asteroid were about to hit the ocean, and the only way to avoid it would be for everyone to, I don't know, jump up and down at the same time, at least half the population will continue to sit on their asses, out of ignorance, apathy, a death wish, or maybe just plain spite. "The other political side wants me to do this, so I absolutely refuse to do it."

So you're jumping up and down... for what? Some marginal improvement in your fitness? So you can say you're at least trying to help? I mean, in that particular case, I'd probably do it, just on the off-chance that everyone else will, too. But they won't.

Yeah, some people are in a position to make improvements now, and I wish them the best. But I'm not in that position. What we need are big, systemic changes, not that one extra dollar.

I can travel less, reducing my carbon footprint.

I can move to a plant-based diet, helping the environment while reducing animal suffering.

I can drive less, walk more. (I know this because I spent over a year without a car.)

I can volunteer my time to causes I care about.

I can mentor youth, sharing my vast intelligence and infinite wisdom with the impressionable younger generation.

Yes, I can do all these things.

But I won't.

FINAL DAY! 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.

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