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Monday, May. 6, 2024

4:28am 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

about 20 hours 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

a day ago
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

April 25, 2022 at 12:02am

#1031312

Branding

The penultimate entry into this round of "Journalistic Intentions"

[18+]:

Bobcats are fighting pythons

Actually, I just like saying "penultimate." Kid Me took a while to figure that one out, because it was before the internet and I never could be arsed to open a dictionary for a word that gets used so rarely. So for a long time I thought it was a synonym of "ultimate," like how "inflammable" means the same thing as "flammable."

Speaking of English weirdness, the sentence up there is ambiguous again. Are bobcats really pythons who are fighting? That would certainly be surreal. I like it. Let's go with that. Oh, wait, no, I guess the bobcats are fighting against pythons.

Pretty sure there are a few high school sportsball teams called the Bobcats. Are any called the Pythons? Probably. There are a lot of high schools in the US, and sometimes you have to get creative with the names. I went to two high schools, in succession. I didn't move; a new school got built and I was in its district. We all got to vote on the name of the new school. Now, what you need to know is that the mascot of the elementary school I attended, which didn't have organized sports (and they never let me play the disorganized ones because I was a nerd), was the Little Indians. You'll see why in a second. The middle school was the Spartans, for some utterly obscure reason. And the first high school was the Indians (which of course explains the elementary school mascot). So, two years into high school, and I never got to be at a school whose spirit animal was... well... an animal.

I should point out right now that yes, of course these days we understand that a lot of "Indian" type mascots are horribly racist. However. The high school's nickname was chosen in acknowledgement of the local tribe. As soon as people started seriously questioning things like "Redskins," naturally (and appropriately), they started to question that one as well. So they did the right thing and actually asked the tribe, many of whom had gone to that high school.

Basically, the tribe said, "We like the name, but lose the feathered headdress. That's not even historically accurate." So they changed the logo but kept the name.

Anyway. As I was saying, after two years as an Indian (the mascot, not the heritage), they went to choose a name for the new high school and had us vote on it. Whether our votes were fairly counted is a question we will never know the answer to, but at least they pretended to give us input into what the school would be branded as. This being before the Internet, no one suggested "Schooly McSchoolFace." But, as it was 1981 and all the cool kids were reading X-Men comics when we weren't fanning ourselves over Star Wars, we (supposedly; I'm still not convinced the vote was fair) collectively decided on the Wolverines.

So even though I finally went to school with a nominally animal mascot, I knew, deep inside, along with all the other kids who voted for that name, that it was actually named after a fictional Canadian mutant antihero whose only connection to anything in the area was... well... nothing.

Hey, while we're on the subject of mascots, there's a professional sportsball team nominally out of New York called the Jets. They're actually based in New Jersey, though, which is yet another example of how New Jersey gets fucked out of the spotlight in favor of a few islands to its northeast. But I digress. Would it really be too much to ask that another NFL team change its name (the team formerly known as the Redskins had the chance, but blew it) to the Sharks?

I mean, come on. That would be awesome. You know that would be awesome; admit it. Jets. Versus. Sharks.

4 Like • Comment • View 7 comments

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