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Tuesday, Jan. 7, 2025

2:29am 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:

tj in a winter wonderland

about 10 hours ago
In response to "Business or Pleasure?"

What instantly pops into my mind when I read "bleisure" and "frolleagues":

Frolleagues, an untreatable diseases that results in a severe rash, blisters, and bleisures.

2 Like

Wordsmitty ✍️

about 14 hours ago
In response to "Business or Pleasure?"

Bleisure with frolleagues. Sounds like kinky porn.

"Nichols, who travels frequently for work, said bleisure is a great way to get the most out of his business travel." and "He still uses all of his vacation days and views bleisure as a "supplement."" - So "b-word" really means taking advantage of your company for extra days and paid expenses, and hoping you don't get caught and fired. Just going out after your business is done each day is one thing. Extending days at the company's expense is another.

2 Like

tj in a winter wonderland

Jan 4, 2025 at 7:32pm
In response to "Giant Red Flag"

My thoughts were, purchase a bundle of the little red flags they stick in the ground for construction markers and just hand some out to everyone I meet.

2 Like

Leger~

Jan 4, 2025 at 12:00pm
In response to "Giant Red Flag"

Pic of the t-shirt on you or it didn't happen.

3 Like

🌖 HuntersMoon

Jan 4, 2025 at 9:44am
In response to "Giant Red Flag"

Elisa: Snowman Stik - Now, let's talk about procrastination...

2 Like

Elisa: Snowman Stik

Jan 4, 2025 at 8:19am
In response to "Giant Red Flag"

Don't worry (or worry). I'll be offering my perspective on this link this year, likely March or April.

2 Like

tj in a winter wonderland

Jan 3, 2025 at 3:09pm
In response to "The Year in the Sky"

It all sounds very interesting and hopefully I will be able to keep an eye on the sky and see some of these. It seems more often than not, it's overcast, or has been for past celestial events. I did, however, get a chance to view the Northern Lights around four this morning. The sky cleared sometime during the night and Max, my Husky woke me up to go out and we enjoyed a few minutes of a spectacular light show.

3 Like

Robert Waltz

Jan 3, 2025 at 11:00am
In response to "The Year in the Sky"

🌖 HuntersMoon

, depends on definition. Astronomically, it's a moon. Astrologically, it (along with the Sun) is a planet. Anyway, I read that to be "planetary parade plus Moon," but we can chalk it up to Lifehacker being misleading again.

2 Like

🌖 HuntersMoon

Jan 3, 2025 at 10:52am
In response to "The Year in the Sky"

Regarding the "planetary parade." The moon isn't a planet. It's a moon.

2 Like

Elisa: Snowman Stik

Jan 3, 2025 at 10:46am
In response to "Marguments"

Oddly enough, this entry rolled out the day the squid and I visited Kennedy Space Center. There was actually a Nars rover model we saw with an interesting note on the information plaque: Not funded by taxpayers dollars.

Ultimately, I feel like while the issue of science communication has seen some improvement, a new problem is emerging. Many communicators have not shown an inclination to have public dialogues with groups who question why we're doing things like going back to the moon. There's been no validation of these concerns by science communicators, which is in my opinion not a good look. And lest you think it's a certain demographic with these objections, well, that's a bias that deserves a re-examination thanks to this piece: https://www.cnn.com/2024/01/05/world/peregrine-moon-mission-navajo-nation-object... remains-scn/index.html .

1 Like

January 5, 2025 at 9:04am

#1081970

Revisited: "Stuck in Committee"

As has become my custom on Sundays here, I rolled the dice and came up with a past blog entry to give it another look. This one isn't that old, from April of 2023: "Stuck in Committee"

At the time, I was on a random road trip. We all know I like to play with randomness, but I'm not sure if I've explained how I apply that to a road trip.

Well, simply put, there's a website (there might be an app for it, but I haven't bothered) that will generate a random point on a map within a user-defined radius from another point. The site returns lat/long coordinates, which get pasted into Maps. Then you figure out where the closest road is to that point and drive to it. If you're feeling adventurous, you can try hiking to the exact point, but around here, that's a good way to get shot.

There are, of course, other ways to do this. And you might have to account for a point ending up in an ocean or lake (which happened to me on the last leg of that particular trip). I expect some people find the idea silly; just pick a destination, already! Well, not me; I like the randomness. Most of the time.

From that earlier entry:

The town I was in was, if you care to look at it on a map, Wytheville, VA. I'd never spent any time in it before, but it's exactly what I expected from a small town in the mountains: two stoplights, 500 people, 600 churches, and a rustic nonfunctional clock on the courthouse.

Some of that might have been hyperbole.

And yet, the beers were named traditionally women's names. Like Rosie, Julia, Edith, etc. Which is fine; it's good to have a theme. But one thing disappointed me: there was no beer named Kate.

You see, I like to order tasting flights, which usually consist of 4-6 sampler-sized beers. The missed opportunity was that I could have had my Kate, and Edith too.

I will just pause while you absorb the greatness of that joke.

There's also the one about how you can't have your kayak and heat it, too.

Here, I found a couple of breweries in Chester, which is a city south of Richmond but north of Petersburg. No, it confuses me, too; as far as I'm concerned, all those cities and everything else in the vicinity is Richmond. There really ought to be a rule: unless there's a significant river (the James doesn't count) or a lot of trees and/or farmland in between, just fucking merge the cities.

I still feel strongly about that. It may be nice for the locals, for whatever reasons, but it's intensely confusing to outsiders (which may be the point).

I saw a wake of buzzards.

The entry goes into the difference between a wake and a committee, which depends on whether they're dining or not. And apparently, though I didn't note it then, if they're flying in formation, the collective noun is kettle.

Don't ask me; someone just made up what a group of something should be called, and people ran with it. I don't really know why. That's how we get a murder of crows or a clowder of cats. The best collective nouns make a kind of linguistic sense, though. Or at least maybe they rhyme or alliterate. Plus, it's boring to call everything a flock, pack, or herd.

Doesn't matter. I'm only pointing this out so the entry title makes sense.

And I don't know when I'll do another random road trip. Almost certainly not before this blog runs out of room.

5 Like • Comment

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