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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 เลียม Enga

a day ago
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

a day ago
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

JayNaNoOhNo

Nov 5, 2024 at 1:16pm
In response to "Anomalies"

*Toronto, Canada submits a sternly-worded petition and disputes the center of the universe claim.*

2 Like

May 26, 2019 at 12:22am

#959630

Save Game

Share an instance in your life when you would have liked a do-over.

There's a primitive computer game called NetHack, which has its origins back in the days of DOS, monochrome monitors, and ASCII graphics. It's a dungeon-delving game that takes its inspiration from early editions of D&D; you play as a protagonist on a quest to recover a specific artifact for your deity. Along the way, you fight monsters, explore dungeons (randomly generated), solve puzzles, and avoid traps, much like in D&D.

Lack of graphics aside, the primary thing that sets NetHack apart from other computer games is that there's no save function. What I mean is, you can save a game and come back to it later if you need to, I don't know, sleep or work or something; but you can't come back to an earlier save point if your avatar dies in the game.

Of course, there are workarounds for that, but they go against the spirit of the game; it would be like cheating at solitaire. You're supposed to play the game, figure things out as you go along, and if you die, all you can do is start over with a different character - but with the metaknowledge you've gained as a player on the previous run. It's a challenge, but that's why I play games. (There's also a wizard mode where you can figure a lot of things out without dying, and that's not considered cheating, but the results of any wizard mode games don't "count.")

By contrast, most modern single-player games - Fallout 4, for example - let you save at almost any time; if you run into a battle it turns out you can't handle, you don't have to go all the way back to the beginning. You reload a later save, and hopefully prep for the battle more effectively. This is good, because while a NetHack game can take 24 hours (and let me tell you, nothing sucks more than dying just before you're about to turn the artifact over to your god), a game like Fallout can take 24 days or more.

I mention this because it's possible that no one thinks about do-overs more than gamers. However, we're painfully aware that, in life, there are no save points, no do-overs, no coming back from battles we can't handle.

But you know, I'm okay with that. While there are many things I wish I'd done differently, if I were magically (or scientifically) handed the opportunity, I'd have to decline. That's because there are only two possibilities I can see:

1) I would have memory of both the original event and its do-over - in which case, I'd give it a 50/50 chance of the do-over making things worse; or

2) I would have no memory of the original event, in which case I'd just want another do-over.

Every mistake I've made has helped make me who I am, so even though it's a fine exercise to think about how we might have done things differently - it helps with similar situations in the future - as with most wishes, the reality of it could never live up to one's expectations.

1 Like • Comment • View 5 comments

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