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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:

Kåre Enga in Udon Thani

a day ago
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 in Udon Thani

a day ago
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 in Udon Thani

a day ago
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

a day ago
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 of House Lannister

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

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:14pm
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:11pm
In response to "Cash Stash"

The discussion of money is an interesting one. Remember the recent collapse of a few banks? I think it was about a year or so ago?
Yes, deposits were FDIC insured up to $250,000 per depositor. But some people and companies had more money in that bank than the FDIC was insuring.
I never followed up on what happened to those people. I don't run in circles of people who own that much cash.

My accounting professor took half a period to explain to us what happened and how the bank went from Silicone Valley darling to dead so fast.

He also told us that the value we give money is not backed by anything except our hope and faith that our economy will keep going.

We didn't discuss whether the value of money needed a lower income class of people.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:04pm
In response to "Revisited: "Hack This""

In my last psychology class, we discussed the evolution of the brain. It is now settled science that we evolved to have not only larger, but also vastly more powerful brains than most other animals because we learned how to cook (process) our food.
Although we are only about 1/4 to 1/3 of a normal gorilla, we eat half of the calories in a day. Not only that, we prepare the food in a way that we get to use more of the calories that we ingest.
The result is that our brain takes up more space in our noggin than a gorilla brain takes up in his noggin. Not only that, each of our brain cells is smaller, so we can fit exponentially more of those into our head.

Now, using all that goodness ...

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 2:58pm
In response to "Hope for Hops"

Wait! Why are beer and coffee affected by climate change? That wasn't supposed to happen. All we had to do was have a boat by the side of the house for when the sea levels rise and beg our property insurance to cover fire damage. How are we supposed to remember all of that if we don't get coffee to wake us up in the morning so that we can think and beer at night to dull our sense of doom?

December 16, 2020 at 12:15am

#1000304

Chocolate-Covered Crap Remains Crap

"30-Day Blogging Challenge ON HIATUS" [13+]:
16. National Chocolate Covered Anything Day
Sounds like a great to 'pig-out' and enjoy!
Have you ever eaten anything 'unique' covered in chocolate?

"JAFBG" [XGC]:
Congratulations! You get to kill one holiday song and never have to hear it again. Which will you choose?

One? Just ONE? Hardly worth it when there are so many that send me into paroxysms of grumpiness.

You know what my favorite thing to have covered with chocolate is?

Chocolate.

And I don't mean milk chocolate, or the abomination that is deceitfully called "white chocolate." There is absolutely no reason to sully the purity of chocolate with any other ingredients, except for a small bit of sweetener.

Which is not to say I don't sometimes enjoy chocolate-covered something. I'm fine with truffles, and it's okay to coat almonds with chocolate. Drizzle some on a dessert, fine. But to me, nothing beats the sublime goodness of pure, unadulterated dark chocolate.

Every year or so, someone will come up with a list of peoples' favorite commercial candy bars, and every damn time, Reese's makes it to the top of the list. As I noted in a previous entry, I utterly despise peanuts, although I'm okay with peanut butter. But to me, that crumbly, sugary, dried-out crap in the middle of a Reese's cup bears little resemblance to actual peanut butter. Okay, I can accept - have accepted - that my tastes are weird, as I've noted in a recent entry. But I simply cannot comprehend how popular Reese's cups are, with their fake, sugary "peanut butter" and waxy milk "chocolate."

I do have weaknesses, of course. Many of them. One of them is, or rather was, Oreos. I think I've mentioned this before, but it's been a while, so I'm going to relate this again:

Used to be I'd go to the grocery store and, in the course of perusing the aisles, the Oreos display would draw me like a moth to a flame. I'd get the standard Oreos, and go about my business, and then at home occasionally eat some of the Oreos.

Then Nabisco started doing different flavors of Oreos. The chocolate-filled ones were good, I thought. And then they came up with fudge brownie cream filled Oreos and OMG those were delicious.

Then they stopped making them. I suppose Nabisco thinks that if they keep coming up with new flavors, people will buy more Oreos. Not me. Once I tried the fudge brownie kind and then couldn't have them anymore, instead of occasionally buying Oreos, now I *never* buy the little fuckers.

Good for me. Bad for Nabisco. Doesn't seem to bother them much, though, as they continue to produce ever-weirder concoctions, the most egregious of which were -- not joking here -- Swedish Fish Oreos. Look, I have nothing against Swedish Fish, and I'm fine with original Oreos, but that combination just strikes me as being particularly heretical, like mixing Skittles with M&Ms.

Anyway, the point is, when it comes to chocolate, I'm happy to try different things; we have a chocolatier here in town that I can say with some certainty is one of the best in the world, and I've enjoyed nearly everything I've had from them. They are expensive, though, and my go-to gift for people who don't drink booze is a box of those chocolates. But of all of them, my favorite is still the pure chocolate ones, sans nuts, sans cream, sans goddamn cherries.

All of this is to point out that yeah, my tastes are obviously different from most peoples'. Another thing I shun with every fiber of my being is commercials, as I have also noted here before. I despise them with an all-consuming fiery passion. And yet... and yet... on Monday, I went to my optometrist. I had to Uber over there because they were going to dilate my pupils and I wouldn't be able to drive back, so in an abundance of caution, I ended up getting there half an hour early. Sitting in the empty waiting room (they've got anti-contagion protocols in place), I was subjected to a holiday music radio station.

I could feel my blood boiling, my lymph roiling, my brain recoiling. As with chocolate, I get that other people have different likes/dislikes than I do. That's fine, I get that, you do you, whatever. But that day, listening to one sappy, gooey holiday song after another, all I could get through my mind was: "Please go to commercial. Please go to commercial. Please go to-" And then finally they did. So yeah, it's official: as much as I hate commercials, I hate standard holiday music even more. Though I could argue that holiday music *is* a commercial.

And yet, in defiance of my wishes, it's still produced and broadcast. Like Swedish Fish Oreos. The only difference is, if SFOs are sitting out on a table somewhere, I can -- and will -- choose not to eat one. Or if there are M&Ms in a bowl and I can tell that they're the bloated, hated peanut kind rather than the inoffensive milk chocolate or delicious dark chocolate kind, again, I can simply pass them up. More for the people who like them, right? Not so with holiday music. It's out there and if I go out in December, November, and sometimes even cocksucking October, I'm subjected to it.

Obviously, a lot of people like it. Fine. And I'll admit that there are some holiday songs that I like. The Grinch theme comes to mind, as you might imagine. And I do appreciate good music, so if it's good music, I don't care if it's holiday or even religious themed; I will appreciate it. The problem is that most of the crap that gets drilled into our collective brains every season is the musical equivalent, to me, of white "chocolate" covered cherries and peanuts.

And I can't think of a bigger abomination than that, except -- maybe -- for Swedish Fish Oreos.

Clearly, I'm going to have to rearrange my schedule so that I get my medical crap taken care of in January, so that I can hermit every December. That way we all win: I don't have to be subjected to smarmy "White Christmas" bullshit, and you don't have to hear me bitch about it.

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