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Monday, May. 6, 2024

6:35am 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 22 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

May 26, 2023 at 11:34am

#1050116

Thirty Years After

Feeling much better today, thanks.

30 years ago, one decision altered the course of our connected world

This article, from NPR, is dated April 30 of this year, the actual anniversary in question.

"Imagine being able to communicate at-will with 10 million people all over the world," NPR's Neal Conan said...

9,999,990 of whom are idiots, trolls, bots, or some combination thereof.

..."Imagine having direct access to catalogs of hundreds of libraries as well as the most up-to-date news, business and weather reports...

Mostly fake, and/or stuck behind paywalls.

...Imagine being able to get medical advice or gardening advice immediately from any number of experts...

And having it turn out to be (sometimes dangerously) wrong.

"This is not a dream," he continued. "It's internet."

And it was fun for a couple of years.

On April 30, 1993, something called the World Wide Web launched into the public domain.

The web made it simple for anyone to navigate the internet. All users had to do was launch a new program called a "browser," type in a URL and hit return.

And then troubleshoot the url typed in, because most people can't spell, and were hopelessly confused by the // thing.

This began the internet's transformation into the vibrant online canvas we use today.

Jackson Pollock's paintings can also be described as vibrant canvases. And any attempts to make sense of those are doomed to failure, or at least false success.

Anyone could build their own "web site" with pictures, video and sound.

And malware.

They could even send visitors to other sites using hyperlinked words or phrases underlined in blue.

Such as this one.

Okay. I'm being deliberately cynical. There's a lot to like about the internet, not the least of which is this website. But the web certainly has its downsides... just like everything else. Later, the article goes into some of these downsides.

CERN owned Berners-Lee's invention, and the lab had the option to license out the World Wide Web for profit. But Berners-Lee believed that keeping the web as open as possible would help it grow.

Well... he wasn't wrong. Fortunately for all of us, CERN was—and is—an international government science research organization, not a private company like ExxonMobil, AT&T, or Apple.

Today, nearly two-thirds of the world's population uses the web to visit hundreds of millions of active websites. Some of those pages belong to companies that are among the most valuable in history like Facebook, Amazon and Google.

None of which would exist without the internet as we know it.

With all of its problems, it's still one of the most influential inventions in history, if not the most. It's difficult to put an exact date on "this is when the internet was born," because there were all sorts of remote networks available before 1993, with many different individual inventors (none of whom were Al Gore), and of course the internet continues to evolve.

But the beginning of the World Wide Web is as good a milestone as any to commemorate.

6 Like • Comment • View 6 comments

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