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Tuesday, May. 21, 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

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 1, 2020 at 12:06am

#994739

Wasted

Let's open October with a prompt from

Journalistic Intentions

(18+)
This is for the journal keeping types that come to PLAY! New round starts February 1!
#2213121 by Elisa the Bunny Stik

This round will focus on weird names! I have worked in fields that have given me access to many bizarre names over the years. They are short prompts for a reason. I really want to see participants flex their mental muscles this round!

I'm not sure if my mental muscles are up to the task. They'd rather sit at home and drink. But I'm going to pick one of these prompts at random and see where it leads me.

Solid Waste Rd.

(You can see the other eccentric road names, as well as the other prompts, at the contest link above.)

I like roads.

Hell, I've designed roads.

Not major ones or anything, but those curvy little subdivision roads with their cul-de-sacs and cookie-cutter houses. I wasn't responsible for the houses. I was only responsible for making sure they weren't going to flood after they were built. Anytime you add impervious surface to an area -- roads, sidewalks, driveways, patios, the houses themselves -- stormwater runoff increases. I'll spare you the details, but the reason why shouldn't be too obscure.

But even runoff coming in from offsite can be an issue, so you don't plan to put houses where this is going to happen. Otherwise, next big storm comes along and your house gets washed downstream. It becomes, in effect, solid waste.

But that's not what I suspect Solid Waste Road was named after.

The other reason I like roads is I like driving on them. They go places and present you with things to look at -- sometimes big things like mountains or deserts, and sometimes little things like street signs.

Because sometimes, as this prompt illustrates, the street signs themselves can be oddball, eccentric, amusing, or head-scratching.

I always wonder what streets and roads are named for. Sometimes, it's trivial, like 33rd Street in Manhattan. Sometimes it's obvious, like Main Street in... well, just about any town in the US. But sometimes, it's a mystery to be solved.

There's a road near me called Turkey Sag Road, for instance. This bugged me until someone pointed out to me that the "sag" part was etymologically related to the "sac" in "cul-de-sac," which means, in French... wait for it... you're not going to believe this in a million years... "sack." Not sure how factual that information was, though.

And yet, I still don't know whether it's named for a hollow where turkeys hung out, or whether someone along the road used to sack turkeys for Thanksgiving or whatever. The internet is completely useless in this regard, and the few people who live in old houses on enormous plots of land along said road do not seem to be the kind who welcome strangers knocking on their doors to ask stupid questions.

Two of my favorite road names are, in no particular order, Clint Drive and Flicker Lane.

I'm sure this makes no sense on the face of it. Perfectly ordinary words or names, right?

Except consider that road names are almost exclusively etched onto street signs in BLOCK CAPS.

And do you know what you get when you put an L and an I together in BLOCK CAPS?

There's an old warning for comics writers, because comics dialogue was also traditionally done in block caps: Never, ever, ever name a character CLINT FLICKER.

Anyway, I'm going to save some of my other road name musings on the chance I'll pick one of the other weird road names in a future entry. I'll just leave you with this: I'd bet $10 that Solid Waste Road leads to the local sewage treatment facility, because that's what they call anything that goes through the sewer system that isn't, well, liquid. And sometimes the stuff that is liquid, but then settles out. It's very tempting to call that "shit," and I suppose in the very general sense of the term it is (as in "What's all this shit?") but actual fecal matter isn't all that's there. No, there's toilet paper, obviously; some of your kids' toys; "flushable" wipes that really aren't; and your ex's wedding ring.

Or it could be a dump, or "landfill." Either way, it's solid waste.

So it's not all that bizarre, really; perhaps someone considered it a bit of a joke ("Okay, we can't call it "Shit Lane," and "Treatment Plant Drive" won't fit on the street sign, so..."); but I'll admit it would be amusing to drive past and see the sign. Still, while it's likely in an industrial-zoned area, I feel a good bit of sympathy for any humans who live along that road. Not only do they have to put up with the fragrance of a dump or a treatment plant, but anyone who sends them snail mail can get a great chuckle at their expense.

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