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Saturday, Nov. 16, 2024

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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:

Write_Mikey_Write!

a day ago
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

a day ago
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

Turkey DrumStik

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

Not gonna lie I need the holiday season chatter.

June 4, 2022 at 1:01pm

#1033351

Beer. That's Why.

Back from the beer festival. Instead of my usual, I thought I'd talk about *gasp* my experience.

So, a little background that I'm not sure I've shared here before: I got the beer fest tickets months ago, when they first went on sale. The theme of the festival was queer beer; that is, not beer that is weird, but breweries that are run by lgbtqia* (or whatever the latest label is) folks.

Now, you may be wondering why I, the most heterosexual man in the universe, would be doing at a queer beer festival. Well, first of all, I've long been an ally, as I'm a proponent of individual freedom. Call it performative virtue if you need to be cynical about it, but I don't think I would be much of an ally if I didn't publicly support these marginalized groups.

The second and more important reason, of course, is beer. Beer doesn't have a gender or sexual orientation. It's just beer. I don't care what the brewer identifies as; I just want to try the beer. A beer festival is a great way to sample brews from all over. And this is the first one I've had a chance to attend since the Before Time.

It might occur to someone to wonder "where's the straight beer festival," to which I'd respond that probably over 90% of breweries are run by straight bearded white dudes, so sometimes to highlight diversity you need to put it out front. Believe me, there are plenty of other beer festivals where the majority can do their thing, too. Or will be; not so much the past couple of years.

Anyway. I was supposed to go with my housemate, but she broke her leg, which of course sucks and tends to keep one from traveling comfortably for a while. As the tickets were nonrefundable, I went with a different friend (after making sure someone else could be here for the housemate).

I do have to say, I was moderately disappointed by the festival itself. A couple of rows of tents on a pier poking the Potomac, with the main sponsor's tent (New Belgium out of Colorado) taking up one end like a throne. Most beer festivals, I get overwhelmed by the choices; here, there just weren't that many. Maybe a couple of dozen. But like I said, minorities are minorities, especially in the beer community, so it shouldn't be surprising that there were relatively few vendors. At least that meant I got to try something from pretty much every booth.

By "try," for those unfamiliar with beer festivals, I mean "sample." Different jurisdictions have different rules; for example, here in Virginia you get four-ounce samples. Apparently in DC it's only two ounces, which is certainly enough to get a taste of the product. So no, it's not like I went from tent to tent having a pint at each. Not even I could have done that. I'd have ended up floating down the river. With no regrets.

After a couple of hours of this, of course we had dinner and went to pass out. Which is how I expected it to go, and why I did warn you today's entry would be delayed.

I expect tomorrow I'll go back to the regularly scheduled program.

11 Like • Comment • View 1 comment

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