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Tuesday, May. 21, 2024

4:51pm 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/

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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:

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

May 3, 2024 at 11:31am

#1070468

It's a Crime

I'll do another one from "JAFBG"

[XGC] today:

What issue do you think has been misrepresented?

Since I pick these at random, I didn't have an axe to grind in mind when I landed on this prompt. It took me a while to sift through all the issues I could remember from relatively recent news stories, eliminate from consideration those that are too divisive to deal with in the short time I take to write these things, and decide on one I gave enough of a shit about to comment on.

An AI could probably have done that faster, and indeed, I considered doing this entry on AI, perhaps even using AI (which is not actually AI, but that's a semantic bugaboo for me and a whole different level of misrepresentation).

Since I was in NYC last week, though, I decided on crime.

No, I don't mean I decided to pursue a life of crime. English is sometimes ambiguous like that, which can be annoying but can also lead to great amusement, so let's not change that anytime soon. What I mean is, I think crime is an issue that's been misrepresented in media, both social and commercial.

The reason I mention NYC above is that there's this pervasive attitude that "big city" crime is a huge problem, and in the US, there's no bigger city than New York. And yet, the reality is, though I can't be arsed to look up statistics, that most of NYC is pretty damn safe. Sure, crime happens... but it can happen anywhere, and if you're a victim of assault or mugging or whatever, the prior chance of you being a victim of assault or mugging or whatever is largely irrelevant.

Discussing this issue is made difficult by how one defines "crime" as well as other factors. Different localities have different priorities. In my experience, law enforcement makes a big show of drug busts, while mostly ignoring crimes with actual victims, such as burglary (yes, drug use is often a bellwether for other crimes, but that doesn't mean it is, by itself, worse than, say, sawing off someone's catalytic converter).

Mainly, though, the issue comes down to one of familiarity. As an analogy, most people in the US drive nearly every day, while they only fly occasionally. The dangers of flying are thus magnified in a person's mind, sometimes to the point of actual fear of getting on an airplane. Statistically, though, it's clear that you're much safer on a jet (even if it was recently made by Boeing) than you are driving to and from the airport. Likewise, someone from a medium-sized town like mine might be wary of the Big City with all its reported crime, while being used to the risks in one's hometown.

Similarly, when it comes to threats to your family, other family members (or former family members) are much more likely to be the problem than some stranger.

And then you get the politically-charged rhetoric about letting in immigrants and the like, who, according to the opponents thereof, are either lazy and want handouts, or are so willing to work hard that they're taking all our jobs; either way, though, they're perceived as potential criminals, which ignores all the US-born criminals who are much more likely to be the ones who do you some harm.

It's understandable to be concerned for one's safety. And it pays to take reasonable precautions. But listening to the media might give a person a warped view of where the actual threats to it are coming from.

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