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Tuesday, May. 7, 2024

1:48am 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:

🌕 HuntersMoon

a day ago
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

Simply Me

May 3, 2024 at 11:58am
In response to "It's a Crime"

I get it. The fear spreading jerks wants us to have an "us vs. them" attitude. The division gives them leverage. (they think)

1 Like

🌕 HuntersMoon

May 2, 2024 at 11:37am
In response to "Butt Of Course"

My wife tried waterskiing once... called it the 100-yard douche.

Talk about retaining water...

2 Like

Elisa the Bunny Stik

May 1, 2024 at 10:53am
In response to "Mad as Hell"

"But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation."

This is a line that must be regarded with care. After all, there are people that get angry about the way they are being treated on a large scale and harness that anger to change their circumstances. There is some level of manipulation in this angry but still legitimate flavor of activism. We do have to consider the possibility that this angel's usefulness can have net benefits (such as environmental cleanup and protection; see the Live Canal as an example).

GeminiGem survived GoT

Apr 29, 2024 at 1:53pm
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

October 20, 2022 at 12:02am

#1039439

Against the Grain

This is just something I thought was interesting.

This Nearly Lost Ancient Grain Tradition Could Be the Future of Farming
A past global staple you’ve never heard of, maslins are poised for a comeback.

And yes, I'd never heard of maslins.

And instead of sowing the seeds of a single grain in orderly rows, spread a mix of grains all over the field, “mimicking nature so crops have random distribution patterns, as in natural forests,” he says. Once harvested, these grain mixtures could be turned into many things: nutritious bread, a kind of roasted-grain trail mix called kolo, beer, and the potent clear spirit known as areki.

You had me at beer.

“We’ll plant the things that go together and are compatible with each other,” Zemede says. “Our farmers are good at mirroring nature.”

One might ask, if you're just going to mirror nature, why not just take what's already in nature? Well, there's just not enough of it for our teeming masses.

Ethiopia is one of the few places in the world where farmers still grow maslins, the general term for different varieties and species of grain that are sown in the same field, or intercropped. Maslins sustained humans for millennia, possibly predating the rise of agriculture more than 10,000 years ago.

Predating or predicting? Or was it a step in that direction?

These grain mixtures tend to be more resilient to pests and drought, and to lend more complex flavors to breads, beer, and booze.

And now I want to try some.

Worldwide, maslins fell out of favor long ago, replaced nearly everywhere by sprawling, single-grain monoculture—but a small and passionate group of scientists, including Zemede, is hoping to change that.

There are, of course, advantages to monocultures (the article goes into that a little bit), which is why people plant single crops in the first place.

The fact that maslins are grown today only in Ethiopia and pockets of Georgia, Eritrea, and a handful of other countries belies how widespread they once were.

One of those countries is not like the others...

One time, I was in Vegas and found out a dealer was from Eritrea. "Do you know where that is?" she asked, clearly expecting ignorance.

"East Africa, near Ethiopia," I said.

She was, indeed, surprised. Look, I don't know everything, but I'm pretty good at looking at maps.

Today, Ethiopian farmers are feeling the pressure to grow modern monoculture crops, thanks in part to a national push to become an agricultural powerhouse. “If you export grains, you want them to be uniform,” says McAlvay. “The global market wants a certain type of wheat for their Wonder Bread. A mixture of three varieties of wheat and four varieties of barley with some other things thrown in really doesn’t make the cut.”

The obvious problem there is that Wonder Bread is basically shit.

The grain mixes also appear to have natural resistance to pests, from insects to fungal diseases. While a pest adapted to attack one species of grain will have a field day, no pun intended, when set loose in a monoculture crop, it won’t be able to jump from plant to plant if the individual it attacks is surrounded by other kinds of grain, McAlvay explains.

No. Own it. Own that pun. Revel in it.

There's a lot more at the article, which, like I said, is just something I found interesting. I just hope I don't have to go all the way to Ethiopia to try the beer.

2 Like • Comment • View 1 comment

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