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Tuesday, Jul. 2, 2024

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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

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Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

tj ~ endeavors to persevere!

a day ago
In response to "Revisited: "Rock you like a...""

I also purchased a generator because our power would go out anytime the wind blew. It seems to have worked, we seldom have power outages now. Living in Minnesota, all we get when the hurricanes push threw are thunder storms and rain. But, it's Minnesota, so thunder storms and rain are normal. This year does seem to be rainier, however.

I'm thinking, after reading this, that I should invest in a couple of rain barrels and bottle the water up. I could probably sell it online to drought stricken people.

1 Like

Kåre Enga in Montana

Jun 29, 2024 at 2:16pm
In response to "Je Voyagerai"

I once was allergic to going on a cruise. But... I should... just for the experience. I've gotten out of my comfort zone for experience.

With the crush of tourists these days any travel should include how much you want to put up with "other people's vacation" as opposed to your own.

1 Like

Lazy Writer est 4/24/2008

Jun 29, 2024 at 1:38pm
In response to "Je Voyagerai"

Happy traveling..be safe.

Elisa: Middle Aged Stik

Jun 29, 2024 at 11:12am
In response to "It Ain't Wrong"

Ain’t apparently begins as amn’t, a contraction for am not, which you can still hear in Ireland and Scotland today

I mean, an abundant number of Scotch and Irish immigrants ended up in the American South, so this tracks.

While a lot of people consider ain’t improper, it’s a very regular and legitimate part of many forms of English, including in Black English (AAVE). Be mindful that judging someone’s use of ain’t as “wrong” can be a very socially loaded act, to say the least.

For some reason, this reminds of one of the reasons I stopped reading Ask A Manager. A bunch of people were getting real uppity about the use of the phrase "baby daddy". Unsurprisingly, many of these people appeared white. One Black person in the comments finally had enough and threw down with this remark:

"I gotta say, as a black woman it grates to have phrases that come out of AAVE be appropriated, assigned negative connotation (likely because they come from black culture), then discarded with prejudice. If you’re using the phrase to conjure up stereotypical imagery, I can get on board with putting an end to that. But there are plenty of people for whom baby daddy or baby mama are not pejorative at all, just descriptors of the relationship in their dialect, and correcting them to “Father of my child” is just another case of denigrating minority speech patterns and legitimate AAVE grammatical constructions and upholding “white is right” standards."

(For more context, check out this link

1 Like

🌕 HuntersMoon

Jun 28, 2024 at 10:54am
In response to "It Ain't Wrong"

Ain't you on a roll today...

3 Like

Adherennium Dr of Phoolishness

Jun 27, 2024 at 11:53am
In response to "Wave Rider"

Horrifying fact, I once painted a reproduction of the Hokusai wave on our bathroom wall. Eventually of course it was painted over, but I like to fantasise that in some distant future it will be archaeologically excavated and held up as an example of early cultural appropriation, (badly executed too.)

1 Like

Annette

Jun 26, 2024 at 8:16pm
In response to "The Oz Hypothesis"

The nekked wimmin look like something that I might have drawn in first grade.

1 Like

Aiva Raine

Jun 25, 2024 at 10:16pm
In response to "Can't Spell Success without Sucs"

Ok- this made me truly LOL- "sipping a gin and tonic made with low-paid laborer tears"

Thank you. Totally agree with the rest of your article.

Money doesn't solve all problems but it sure as hell eliminates many and makes it easier to go places or buy things that can create some happiness. IE- a property somewhere quiet and peaceful and a trailer with which to chill on said property.

Rich people are typically clueless assholes.

1 Like

Anni Pon

Jun 25, 2024 at 9:30am
In response to "Can't Spell Success without Sucs"

I've never heard anyone say, "That guy is so successful, but he doesn't really make much money." Or anything similar. Sure, you can have a positive impact on the world without making lots of money, but people won't call it success.

2 Like

Annette

Jun 23, 2024 at 1:28pm
In response to "Revisited: "Experience""

This is how I coped:

1 Like

June 30, 2024 at 7:40am

#1073352

Revisited: "Rock you like a..."

Today's retrospective takes us back to September of 2018, a brief entry about the weather: "Rock you like a..."

So now, six years less a season later, how have things changed?

It's hard to avoid people talking about the impending doom of Hurricane Florence, so I might as well add my voice to the babble.

I remember that one. While it hit the coast as a Cat 1, it was so slow-moving that what it lacked in wind damage it made up for in massive flooding.

No, I'm nowhere near the coast. Looks like the worst we'll get is a bunch of rain. Nothing new there; it's been raining more often than not all summer. I'm at a high spot and I have a sump pump and a backup generator.

I swear my sense of time is horribly distorted. If you asked me yesterday when I got my generator, I'd have probably answered, "I don't know. 2020, maybe?" Our power sometimes goes out in a light breeze, so it's not just for hurricanes. I justify the presence of the (very loud) generator by claiming I have a medical device that requires electricity, which is true, but the main reason is I don't want to be without internet for more than five minutes.

I also have a house surrounded by trees, though, so I might be boned anyway.

Since then, I've had at least one of the trees taken down, one that was leaning noticeably toward the house. Still boned when the next 'cane blows through.

Some good friends of mine live in Raleigh, NC. They're boned.

They got through it just fine. Couldn't go anywhere for a day or so, if I recall correctly, but safe and dry. They just bought a house in southwest Virginia this year, which means the next hurricane will head for them. And yes, hurricanes can still do significant damage that far inland. Not as often, but it happens.

I have a fondness for Virginia Beach and the Outer Banks. I'll miss them.

My fondness for Virginia Beach ended when I heard that my favorite watering hole there was closing. And miraculously, most of the OBX is still there. I just spent a night there last year.

It seems like a lot of the places I've been to have been hit by something.

Some sort of familiarity bias. Also, I travel more than a little, and every time I do, the chance of a place I've been getting smacked by some disaster goes up a little.

Well, as long as Las Vegas is still- wait, what? The Colorado River is at historic low flows, and Lake Mead is dangerously dry?

Since then, the water level there has fluctuated,

but it's still pretty low. I also haven't been to Vegas since the pandemic started.

I'd ship 'em some of our rain if I could. Let me tell you, if I ever hear another breath about "drought" around here, I'mma lose it at someone.

We've had a bit of a dry spell this year (I write this during a drizzle, however, and we're supposed to get thunderstorms this afternoon and evening). My grass is partly brown. Good thing I don't live in an HOA; I refuse to waste water on lawn irrigation.

They've been predicting a very active hurricane season this year, but those long-range predictions are questionable at best, so I don't pay much attention to them. Weather is notoriously hard to predict with any accuracy more than a week out, so I'll do what I do every year: wait and see.

And try to remember to get my generator serviced.

1 Like • Comment • View 1 comment

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