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Wednesday, Nov. 13, 2024

1:12am 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

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:

Brandiwyn🎶

about 14 hours ago
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

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

September 16, 2024 at 9:42am

#1076872

Two Much

We all know I like Cracked. This is partly because, like me, they try to be amusing and informational at the same time.

Sometimes, that doesn't work out on one front or the other.

Companies That Make Only Two Wildly Different Products
It’s usually a bad idea for, say, a coffee shop to start selling auto parts

As a business, diversifying your product line is a surefire way to grow your customer base...

Not always.

Some companies, however, decide that they do two things. Two things only. Two wildly different things only.

5. Guinness

It’s not just a coincidence of nomenclature — the Guinness Book of World Records is the same Guinness that produces the world’s carbiest beer.

No.

I mean, yes, originally. Guinness reportedly started the World Records book as a way for pub-goers to settle bets, as the article notes. Later, the publication (which I'll call GWR) got sold to another company, with rights to the name.

That company then eliminated every world record related to drinking, on safety (read: liability) grounds.

While I understand their reasons, this ripped them from their roots. Would you call a piece of paper and a tree the same thing? No. Then GWR has nothing to do with the Irish manufacturers of dark and delicious malt beverage.

Guinness, the brewer, also sells merchandise, and even has showrooms for it. I've been in one in Las Vegas. Well, at least they did pre-pandemic, and I can't be arsed to see if they're still doing that. Point is, though, not only is GWR no longer affiliated with Guinness, but even if they weren't, Guinness would be selling more than two products.

4 Coors

Yep, the company that makes beer as cold as the Rockies is also involved in the production of high-tech ceramics.

I would argue that they don't make beer, but I'm admittedly a snob on the subject.

Also, it's Molson Coors now, and they suck even harder than AB/InBev, which at least has the decency to (mostly) leave craft brewers to their own devices when they Hoover them up.

3 Yamaha

The customers for Yamaha keyboards and motorcycles couldn’t be more different, and technically, they’re not the same company.

As noted, they're not the same company, so this shouldn't count, either. Also, why can't bikers be keyboardists, or vice-versa?

2 Bridgestone

Bridgestone is another Japanese company that successfully divided itself, not out of prudent business sense but for the love of the game — literally.

Tires and golf balls? Come on, they're both round, dimpled, and made of synthetic rubber.

1 Michelin

Speaking of tires, it’s often said that the Michelin tire company created their restaurant rating system to get people to drive more and wear down their tires faster, but it’s a little more complicated than that.

Okay, I'm going to grant them this one.

In 1900, people had to be convinced to buy and drive cars at all, so Michelin began publishing car-specific travel guides that included where to get gas, what time the sun set at different times of year (because there were no street lights), and yes, the best hotels and restaurants.

In the US, at least, there was another, way worse reason to have to know sunset times.

Now you know, once our car-centric society has destroyed the planet and global warming kills us all, you can blame the French.

Technically, the Industrial Revolution only kicked into high gear after Nicolas Léonard Sadi Carnot figured out the whole "thermodynamics" thing, so we might as well blame the French.

1 Like • Comment

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