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Friday, Nov. 15, 2024

10:52pm EST

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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

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:

Write_Mikey_Write!

a day ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

a day ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

May 23, 2022 at 12:02am

#1032742

Annoying Things

For "Invalid Item"

The most annoying thing about your town/area

Of course there are no annoying things about where I live. Everyone is happy, nothing is inconvenient, and the sun is always shining.

I can hear your "Yeah, right" from here.

As I've noted before, when it's not freezing (defined by me as 55F or below) outside, I like to sit on my deck. I paid a lot of money for that thing and by Marduk's manhood, I'm going to use it.

This is normally quite pleasant. Songbirds are tweeting (and not complaining about Elon Musk), bees are buzzing, owls are hooting (yes, yes, I did my Duolingo lessons; shut up) and crickets are cricketing. Right now, the leaves are lush and green, and blocking the view of the backyard neighbors' houses.

Yes, very pleasant, except during the day and at night.

During the day, everyone gets their yard work done. This wouldn't be so bad if everyone did it at the same time. But no; that would be too kind. The neighbor mows his lawn. Then, when that's finally done, the other neighbors mow their lawn. After that one's finished, one of the people behind me mows their lawn. And then another. And then another.

There's no respite in the non-grass-growing seasons, either. If it's not lawnmowers, it's jet-engine-powered snowblowers or leaf blowers. And sometimes chainsaws. One time, the people two doors down had their ancient elm tree cut down, one of only two in the neighborhood. That took all day so it wouldn't fall on someone's house. And it was loud. On the plus side, I now own the only remaining elm around. One of these days I'm going to have to get it removed, too, and as loudly as possible, because even elms die at some point. I'm hoping to hire an artist to turn the stump into a throne where I can sit, with a beer and a cigar, and survey what's most definitely not my domain.

And then, at night? You can hear further at night for some reason. Probably because hardly anyone mows their lawn after dark. I can hear a passing train right now, and that's nearly a mile away. Well, honestly, that doesn't bother me much; I spent my childhood near railroad tracks, and the rumble and horn are kind of soothing. So that's not really an annoyance, but it does tell me that pretty much anything within a mile is going to reach my eardrums. Like sirens and semis on the interstate. Parties to which I'm not invited. Domestic disputes. Gunshots. Okay, the gunshots are pretty rare, but this is still America.

And also the nightly muscle car race. For some reason, that's still a thing. When electric cars started becoming mainstream, I rejoiced because I thought it signaled the end of the muffler-less disturbance of the peace. But no. People started complaining that you couldn't hear them coming, so they made them purposely louder, thus negating 3/4 of the purpose of having an electric car. Instead of, you know, learning to not walk in the middle of the goddamned street.

Not to mention the sirens. There's almost always a siren somewhere. Especially after the gunshots.

But all those aural annoyances are actually minor compared to the biggest annoying thing about living in Charlottesville:

This town is infested with douchebags.

It's not just the fashion, either; it's the attitude. Entitled, demanding, uncool. This is primarily evident while driving, but I also derive vast amusement from lurking on the local Nextdoor app. Like, for instance, people complaining about neighbors doing loud yard work. Or the latest, some guy complaining about always backing out of his blind driveway into traffic. I mean... have you tried backing into the driveway? Or putting up one of those convex mirrors? Or both? Come on. Or maybe taking out your muffler so they can hear you coming.

My town has not yet instituted a plastic bag ban. I hope they don't; I use those things for trash, and without plastic grocery bags, I'll have to actually purchase small plastic trash bags, thus imposing the same environmental impact but at greater cost to myself. Bans are well-meaning, I'll grant that, but like most of the bullshit people do in response to pollution or climate change or whatever, they don't do a damn thing. Remember when everyone was trying to ban plastic straws? It's like that. Rearranging deck chairs on the Hindenburg. Anyway, the point is, if they do start to discuss one, I have this fantasy about showing up at City Hall with a prepared speech about banning douchebags instead.

Won't happen. Too lazy. But I can make jokes about it.

4 Like • Comment • View 8 comments

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