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Wednesday, May. 1, 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:

Elisa the Bunny Stik

about 11 hours ago
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

Kåre Enga going to Montana

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga going to Montana

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga going to Montana

Apr 25, 2024 at 2:58am
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

Apr 24, 2024 at 4:26pm
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem survived GoT

Apr 23, 2024 at 6:51pm
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

April 15, 2019 at 1:17am

#956598

Vacation

Apparently, I can either play video games, or I can blog every day.

That's okay. I need a break every now and then.

One thing I have been sticking to is my eating less and exercising plan - surprising, because I was sure I would have failed by now. But I keep seeing positive results (that is, negative results in terms of weight), so somehow, I've managed.

That will all change come Thursday.

As this is my blog, I suppose I could provide a bit of background. Feel free to skip it if you don't give a shit.

I was raised in a Jewish family. My mom's side is from New York City. She had two sisters and a brother. One aunt, A, stayed in NYC and never married or had kids. The other aunt, E, moved to Indiana (of all places) and raised two kids there. Now, the religion thing is relevant to the story because A was very religious and we'd often have Passover seders at her place. E, in contrast, has been an atheist since before I was born. (Yes, I take more after E, but I was always closer to A - go figure.) So - bear with me, here - one of E's kids, who is a bit older than I am, moved to Manhattan from Indiana and married a born-again Christian. Later, E ended up moving back to NYC as well.

If you managed to untangle the above genealogy, you'll realize that A was both my aunt and my cousin's aunt, so we had that in common. And being that they were in the same city (albeit a good hour away; NYC is big), they saw each other more than I saw either of them. But some years, we still got together for Passover seders - though none of the rest of us were religious in any meaningful way, I did it for my heritage and my family.

Aunt A died a few years back, right when NYC was buried under three feet of snow. That put the "fun" in funeral, let me tell you. Anyway, ever since then, my cousin's wife - the Christian one - has taken it upon herself to organize a family seder every year, to honor her husband's side of the family, mostly Aunt A. This is actually a bigger deal than it may seem, because doing it right is work, and since Passover usually starts around the same time as Easter (a holiday she observes), things get busy for her. So I respect her for that.

All of which is to explain why I'm going away for a few days. I mean, I'll still be "here," as in I'm bringing my laptop with me, but this is the first real trip I've had since I started the whole weight-loss thing.

So I'll probably be bad. I might even be very, very bad. At a minimum, as you might know, the Passover seder includes drinking four glasses of wine. But since it's been so long since I've gone anywhere - Vegas back in December - I'm planning on taking the opportunity to drive to the vicinity of NYC early, find a brewery to sample, and then, after I see the family, I'm hoping to find even more breweries in the general area to visit. Make it a week - Thursday through Wednesday.

Bastards are probably all closed on Easter, though - but I'm sure I'll find something to do. I'm just hoping that the siren call of the Atlantic City casinos doesn't overwhelm my desire to sample new and interesting beers. We'll see.

When I return - there's a deadline for that as I already have a ticket to Avengers:Endgame on that Thursday - I can back off on the overindulgence again. Consider this a vacation. And maybe I'll pour one out for my Aunt A.

7 Like • Comment • View 3 comments

April 1, 2019 at 12:14am

#955484

Time to Change

So, I've decided to become a vegan and abstain from alcohol.

This isn't out of piety or puritanism, but because I have a need to feel superior to everyone else. I mean, yes, I already am superior to everyone else, but not everyone knows that. It is only by adopting veganism and abstention that it will be blindingly obvious.

I'm already on the way to this; after all, I already consider myself above the petty concerns of mundane life. This will only serve to cement that fact. I can look down my noses at the rest of you apes, secure in the knowledge that My Way is the Best Way.

Oh, hell, I can't do this any more...

APRIL FOOLS!

*chugs a beer*

*eats a rasher of bacon*

*belches*

7 Like • Comment • View 3 comments

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