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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 23 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.

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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 3, 2024 at 10:05am

#1076171

To Love Until I Laugh

"Blog Week Birthday Bastion 2024"

[13+] by WakeUpAndLive~"HoHoHo"

Prompt 3. Sept 3.

You can achieve all the things you want to do, but it's much better to do it with loved ones around you; family and friends, people that you care about that can help you on the way and can celebrate you, and you can enjoy the journey. ~John Lasseter

Your most significant other(s) is/are....! Write about your loved ones (furry or not).

Right, as if I were capable of love.

Okay, okay, that's a joke, and I'm determined not to make today's entry as existentially terrifying as yesterday's. But as I showed then, you can't count on anyone. Just saying. And not just because I was given up for adoption as an infant, either.

Still, "love" carries a lot of baggage and assumptions. The Greeks might have gotten it closer to right by slicing it up into sub-loves: eros, agape, whatever. They say the Inuit have dozens of words for snow. While this is probably false, like all legends, it illuminates what might be a greater truth: the more important a concept is culturally, the more words they'll have to describe its various shades and gradations. We just have two words for love: love itself, and like.

We've got dozens of words for killing, though. And hundreds of words for penis.

All of which is to say that while there are people (and cats) that I particularly care about, I neither have nor want a "significant other." I've been married twice, and you know what Einstein supposedly said about the definition of insanity.

Einstein probably didn't say that, though, and it's not really the definition of insanity.

You know who (probably) did originate that quote, though? According to some of my fact-checking sources, in its current form ("Insanity is doing the same thing over and over again and expecting different results"), it was Rita Mae Brown, in the voice of one of her characters.

Rita lives near me. I met her a few times. Exceptionally nice lady. Cat person. I suspect she found it extraordinarily amusing that her quote became misattributed to the guy whose picture is in the dictionary under "genius."

Well, enough with the name-dropping. If it helps, I live near John Grisham, too, and never met him.

The point is, these days, I'm done with that sort of love. You know how some guys, they'll meet someone of their preferred gender, and their mind immediately fast-forwards ahead to the sex part? Mine fast-forwards to the breakup part, and I don't want to deal with that again.

But I have friends. And cats. That's enough for me.

Because if there's one thing I learned early and took with me into adulthood, it was how to be comfortable being alone. It always surprises me how much other people depend on each other, as if that rug won't be pulled out from under them at some point. Some say the pain of eventual abandonment is worth the pleasure of another's company, but I'm not so sure.

Don't dare think I'm bitter about it, though. I get that some people would be, but I'm not them. Mostly, as always, I'm amused, and laughter is one constant friend I can count on.

Let's do this again. 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.

2 Like • Comment • View 3 comments

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