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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

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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:

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.

May 12, 2022 at 12:07am

#1032266

High-cal Local

"Invalid Item"

All of this traveling has made Andre hungry, and we don't want a Hangry monkey on our hands! So today's prompt is about food, and the best place for our buddy to eat in your town!

What food or foods are your town/area noted for? What's the prevalent cuisine? Where is your favorite place to eat out in your neck of the woods?

I mentioned some of the more important food places (the ones that also offer fine fermented and/or distilled adult beverages) in last week's entry, here: "A Tour of the Town"

. To reiterate, there are several purveyors of glorious nectar that also serve delicious meals.

As Charlottesville is a university town, it attracts a wide range of cuisines. Just off the top of my head, in addition to what can only be described as American food, we have Mexican, Chinese, Thai, Japanese, Belgian, French, Indian, Afghani, Mediterranean, Italian, and several others. There also used to be an excellent South African restaurant (with a bar), but, sadly, it fell victim to the pandemic. That's of course in addition to various familiar fast-food and casual chains.

Oddly enough, one thing we lack is a Denny's. And when I was in college here, we didn't even have a Waffle House. We had to get our late-night bleary-eyed food fix from Hardee's and a local deli that's not around anymore. Now there's a Waffle House less than a mile from me, and I haven't ended up there in years.

You don't "go" to Waffle House. You "end up" at Waffle House. It's right next to a Taco Hell, and I call the driveway between them "Desperation Alley."

While there's no one prevalent cuisine -- though at one time, you couldn't throw a chopstick without hitting a Chinese restaurant -- we're serious about our restaurants here. Someone told me once that we have more restaurants per capita than New York City. That seems to not be the case -- sources vary depending on how one defines the local population and what sorts of restaurants we're talking about, not to mention the ever-changing landscape of food service -- but we certainly have a lot of choice here. Obviously on an absolute basis, NYC has more and more varied eateries, but it's also dealing with over 150 times the population (not counting tourists).

As for favorite place? Well, I don't have one. I try not to get too attached to restaurants, as they flicker open and closed like lighthouse shutters doing Morse Code. I learned that lesson hard a few years ago: my favorite restaurant in the universe was The Raven, three hours away in Virginia Beach. I'm still experiencing grief from its closing. No, stop laughing; I'm serious here.

But if you looked at my credit card statements, a) you'd be appalled and b) you'd see Timberwood Tap House standing out as my most frequent destination, right up there with Alamo Drafthouse Cinema. Both of them are within walking distance of my house, and across a parking lot from each other; they both serve excellent food, and they both have a wide-ranging, varied list of beers on tap.

Of course, I mostly go to the Alamo for movies, but I also find time while I'm there to order food and beer. With Timberwood, well, when restaurants reopened after the pandemic, it became my habit on Mondays to walk over there, sit on the patio, and enjoy lunch with beer and music. Even when it was cold outside.

But I like variety, and those aren't my only destinations. There's a local Mexican chain called Guadalajara, for instance, one of which is in walking distance in the other direction, and of course they also have tequila.

And of course Three Notch'd, the brewery, is only two miles away. I'd walk there even if I had a car, because, well... beer.

I can't leave this without calling out one of my other local regular vendors of victuals: Bodo's Bagels. They have three locations, and some say their bagels are superior even to the ones in New York. To which I can only say: spend more time in New York. Regardless, they're very good, even if they don't serve booze, and even though it is the sort of place where you can hear people complaining at the next table about food as cultural appropriation whilst eating a bacon, egg, and cheese bagel.

And hey, if you get bored with the local fare, Richmond is an hour's drive away, and DC, two.

Now I'm hungry. I'll resist staggering over to Waffle House, though.

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