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Monday, May. 20, 2024

10:24pm EDT

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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:

Aiva Raine

May 17, 2024 at 6:57pm
In response to "Knead Some Dough?"

I grew up on mostly Wonder Bread despite our family having a large dry farm (dry farm being a farm that grows wheat and barley and safflower without irrigation- it relies solely upon mother nature to rain). I was never fond of it and looked forward to the times my mom would laboriously mill and grind the grain we brought back during harvest into flour and make home-made wheat bread. There was and still is nothing better than fresh whole wheat bread with a little butter and honey.

I think we did the Wonder Bread because my mom wasn't a fan of cooking and making bread is a time-consuming process.

I quit doing the white bread decades ago. There are so many kinds of healthy, no HFCS, etc whole grain breads out there that are delicious that I have no idea why any adult would choose the crappy Wonder Bread.

1 Like

Wordsmitty ✍️

May 13, 2024 at 1:18pm
In response to "The Breakfast and the Breakfurious"

And for those who rather not read the Smithsonian article, the History Channel episode that covers Pop Tarts (if you have a cable TV account):

https://www.history.com/shows/the-food-that-built-america/season-4/episode-1

Annette

May 10, 2024 at 12:05pm
In response to "Meditation Clause"

Everytime a stranger asks me to close my eyes, I keep my eyes open to see what they are up to.
Meditation is not for me.

But I think most people would have 45 minutes every day if they took that time away from social media or TV watching.

2 Like

Wordsmitty ✍️

May 9, 2024 at 1:15pm
In response to "Super Stew?"

But . . .

What's the difference between one being in the soup or in a stew? Is one thinner or thicker? How do writers use soup and stew?

1 Like

Elisa the Bunny Stik

May 9, 2024 at 10:11am
In response to "Super Stew?"

"Served in a pot? Maybe in your country."

Honestly, in the US I'd think soup would be served in a pot due to the quantity that ends up being consumed.

1 Like

Lazy Writer est 4/24/2008

May 8, 2024 at 3:02pm
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

May 8, 2024 at 10:52am
In response to "Be Positive"

Asking doctors for advice has its own pitfalls. Because there is no money in recommending a sensible nutrition pattern, they will say things like: Look it up online.

2 Like

🌕 HuntersMoon

May 5, 2024 at 8:50am
In response to "Revisited: "Fail""

Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs

1 Like

Charity Marie - <3

May 4, 2024 at 5:42pm
In response to "Overdraft Dodgers"

I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.

1 Like

Kåre Enga in Montana

May 3, 2024 at 4:23pm
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

October 2, 2020 at 12:02am

#994824

Dark and Stormy

I'm not firing on all cylinders right now. I think I've mentioned this before, but I've been fighting a toothache since approximately 15 seconds after my state instituted lockdown back in March, and it's only been about a month since the pain got so bad that I wanted the pain to go away even more than I wanted to, you know, not get sick -- and I can't think of many better places to get a certain airborne disease than at a dentist's office.

The other thing I've been doing is trying to get a flu shot. My pharmacy advertises them, but every time I've gone there in the past two weeks, they've been conveniently "out."

A root canal - actually, two of them at the same time - was scheduled for yesterday morning, and afterwards, as I went to pick up some prescriptions the endo had called in for me, behold, a flu shot was available. Now, I don't usually get major side effects from flu shots, but I think the combination of having someone dig around inside two teeth, the painkiller prescription for the aftermath, and the vaccine conspired to give me mental fog. It's a bit better now that I've had some rest, but I still don't feel all that coherent. A bit like being drunk, actually, only without the fun part of, you know... actually being drunk, or having drunk. (No, I didn't drink any booze and won't until the meds have run their course.) But I just can't seem to shake the fog right now.

Like, for example... as I've mentioned before, I've been working hard to learn French on Duolingo. The way that site is set up, lessons come in chunks of twenty exercises. Usually I get about 17-20 of the exercises right. I'm sure some people with better memories than mine do better, but hey, I'm slowly improving. Point is, when I went to do the lessons today I regularly flubbed five or six of the exercises for almost all the lessons. Stupid, basic stuff too, like using the entirely wrong word, making a wrong conjugation of a verb, switching genders (too tired to make a joke out of that right now), or typing "tu" instead of "te" when the pronoun is used as the object of a verb.

All of this is to say that I have a lot of things I want to do on WDC this month, and was hoping to hit the ground running; instead, I hit the bed sleeping.

Still blogging tonight, though -- I don't feel quite bad enough to break my streak -- and I expect things will get better once I've had some rest. And sorry if I flub English as badly as I did French earlier.

One of the things I wanted to do this month was a different blog challenge, besides the one I did yesterday, but I just don't have the concentration for it right now. So I'm falling back on my Blog Fodder folder. Here's a Cracked article about one of the most infamous fiction writers of all time.

https://www.cracked.com/article_27980_the-it-was-dark-stormy-night-author-had-su...

The 'It Was A Dark And Stormy Night' Author Had A Super Weird Life

"It was a dark and stormy night; the rain fell in torrents - except at occasional intervals, when it was checked by a violent gust of wind which swept up the streets (for it is in London that our scene lies), rattling along the housetops, and fiercely agitating the scanty flame of the lamps that struggled against the darkness."

How Not To Write, Lesson One.

He also coined phrases that are still used unironically, like "the almighty dollar" and "the pen is mightier than the sword." But, more importantly for now, his life and its consequences were weird as hell.

Okay, those were things I did not know before reading the article. Of course, it's Cracked, so I can't be 100% sure that this is factually accurate, but now it's in my mind as "provisionally true" because in my current condition I can't be arsed to fact-check (though that's not much different from me on a good day). If someone else does that, feel free to comment.

Let's talk about his marriage first, because it'll make any relationship problems you're struggling with seem quaint.

I mean, I'm not going to paste the entire article here, because I don't want Cracked's crack team of lawyers slapping me with a plaig... plege... plegia... copying shit off their site lawsuit. But this stuff is seriously warped.

Now you know what they say about revenge: it's best served repeatedly and with increasing fervor over several decades.

Yes, I believe the Klingons came up with that proverb. In any case, that section deals with the very public spat between Bulwer-Lytton and his ex.

But of course it gets weirder.

But with the worst of their exchange over, Edward could get back to his writing, so now let's talk about the book that led to insane Nazi conspiracy theories.

Again, go to the link for details, but basically this guy, his memory now mostly reduced to a source of parody (I've done my own twists on the "dark and stormy night" thing), was popular and influential enough to affect freaking Nazi Germany a century later. And the echoes still reverberate today.

Bulwer-Lytton did not, of course, live to see any of that, but he did live to be offered the Greek throne.

I told you it got weirder.

Anyway, while that website varies widely in quality, sometimes you find a gem or two. And this particular one has to do with the lingering influence of the power of writing, so here I am, fighting off brain-cobwebs in an heroic effort to share the story with my fellow writers.

You're welcome.

Maybe tomorrow I can do something more coherent.

8 Like • Comment • View 4 comments

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