Search where?

This Portfolio (cathartes02)

All of Writing.Com

◄ March ►
S	M	T	W	T	F	S
					1	2
3	4	5	6	7	8	9
10	11	12	13	14	15	16
17	18	19	20	21	22	23
24	25	26	27	28	29	30
31
Archive				RSS

Offsite Blogs

· Waltz Travel Blog

Create New Item

Read & Review

Community

Browse By Type

Browse By Genre

Writing Resources

Saturday, Apr. 27, 2024

6:05am EDT

Members: 701

Guests: 4,165

Total Online: 4,866

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

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 in Udon Thani

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 in Udon Thani

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 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?

March 15, 2024 at 9:38am

#1066306

Why So Selfies?

Yes, I used to get paid to do photography. No, that doesn't make me an expert. Not being an expert has never stopped me from posting stuff here. This one's from, surprisingly enough, Business Insider.

I take such good travel photos of myself that people swear I have a secret photographer. Here's how I do it.

Like this author, I tend to travel alone and take photographs. There's one important difference, though: never, in the history of the world, has even one photograph been improved by my presence in it, and, more often, it ruins the whole shot. At least once, it literally cracked the camera lens. So, sure, if you just gotta be the focus (pun intended) of every picture, and you're attractive enough to justify it, great. Otherwise, there's absolutely nothing wrong with taking general landscape shots to prove you've been somewhere.

Now, honestly, the article's three-bullet summary should be enough, though even then, the first one is superfluous:

As a solo-travel content creator, I've learned lots of tips for taking great photos while alone.

I always travel with a smartphone tripod and use my smartwatch as a remote shutter.

If I have to ask someone to snap a photo of me, I always take a photo of them first.

So that's all, folks.

...okay, no, I have a few more things to say about the article.

First, the example photos really are good, so she's not just blowing wind, here. The last one, especially, with the cacti? It's the first time I've looked at a nature shot and said, "Wow, this picture really is improved by having a human in it." Mostly because the human is wearing something deep red, which nicely complements and contrasts the other colors in the picture.

Second, she uses her smartphone for the pictures. These days, there is nothing wrong with this. Phone cameras can be remarkably good, now. Fifteen years ago, I might have scoffed at the idea, but not now. There are things you can do with a standalone camera that you just can't with a phone, but they don't involve composition.

On to details:

A smartphone tripod is the No. 1 thing I pack on any trip or hike.

I would think that the phone would be "No. 1," but whatever. Really, that's it. That's the secret. That, and...

I use the Bluetooth connection between my smartphone and smartwatch to create a remote shutter and snap a picture.

No matter the camera, selfies, being by definition shot at arm's length, distort features. Most people aren't going to be that close to you, excepting crowded subways, concert pits, and intimate situations, so you're going to look different. Also, it's rather difficult to get a whole body pic (assuming you have a body worth photographing, and/or an outfit you want to emphasize) that way, even with a selfie stick. So the remote thing is a good idea, I think. I used to use a manual cable. I never could get Bluetooth to ever work reliably on anything, so best of luck with that if you try it.

A few other tips, and then:

There are times when it's not possible to set up a tripod, but I still want to get some photos in a beautiful location.

In those instances, I may ask someone to snap a photo or two of me — and, of course, I return the favor.

One, that's always been kind of a gray area in my knowledge. If someone else uses my phone to take a photo following my basic requested directions, should they get the photo credit? Like I said, I'm not an expert.

And two, I hope you have a backup camera/phone, because not everyone you meet is trustworthy. Most are. But sometimes, you get unlucky.

Now, in a way, this article is an ad, not only for the author's material, but also for the products she mentions. That doesn't mean there isn't something useful in there.

3 Like • Comment

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted Writing.Com, its affiliates and its syndicates non-exclusive rights to display this work.

Printed from https://www.writing.com/main/profile/blog/cathartes02/day/3-15-2024

Site Links:

Resources:

Need help?

Please post questions in
our support forum.

Places of Interest: Unique Wedding Invitations for unique wedding needs. Color Copiers found here.
Baby Names can be hard to pick. Hands-free hygenic toilet seats covers. Dramatic Music rocks.
Vampires are people too. Write Poetry here. Try this Stock Market quiz.
Teaching is a noble job. Get info on Tax Refunds.

All Writing.Com images are copyrighted and may not be copied / modified in any way.
All other brand names & trademarks are owned by their respective companies.

Generated in 0.63 seconds at 6:05am on Apr 27, 2024 via server web1.