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Sunday, Nov. 17, 2024

1:27pm EST

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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

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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:

Turkey DrumStik

a day ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

Nov 14, 2024 at 12:10pm
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

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

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