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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.

May 5, 2022 at 12:03am

#1031944

A Tour of the Town

"Invalid Item"

Today's Prompt For Home Sweet Home Blogging Challenge!

If Andre visits your Town, what are some places/sites/locations he should visit?

2. Famous locations or places to see in the town/area

I'm new to the Banana Bar, but I know two things about Andre:

1) Andre is a monkey.

2) Andre likes to drink.

Now, here in Charlottesville, we don't discriminate, so (1) shouldn't be a problem. I will, however, avoid taking him to see the parks, as some of them have playgrounds with monkey bars, and I don't want anyone to think I'm caving to stereotypes.

As for (2), well, Andre... you're in luck. This is my specialty, my bailiwick, my lane, my raison d'être.

Let's start downtown. On the historic pedestrian street called the Downtown Mall sits one of the few establishments that has been here longer than I have: Miller's.

Now, one thing you need to know about Virginia: There are no bars in Virginia. None. Zero. Nada. Zilch. We don't have a single (legitimate) place of business that exists for the sole purpose of relieving patrons of their money in exchange for distilled beverages. There are laws against that sort of thing. (Some craft distilleries allow for sampling, but they're still not technically "bars.")

What we have are restaurants that happen to serve alcoholic beverages from behind a counter festooned with stools.

Miller's is one such restaurant. Its claim to fame, other than sheer longevity? Dave Matthews used to tend bar there.

Just down the street we find The Bebedero. It's in a new location, but it still serves excellent Mexican food and -- this is the important part -- tequila. Real tequila, not that 51% de agave pisswater with caramel coloring.

Near Bebedero, and owned by the same righteous dude, is The Whiskey Jar. As its name suggests, its specialty is whiskey (and seasonally varying food), though they also have some whisky. And maybe a few things that sometimes get mixed with whiskey and whisky, but why bother when you can sample, neat, some of the excellent single-malt scotches and premium bourbons? No Pappy Van Winkle, sadly, but plenty of other fine distillations.

And oh, I could go on. One thing we don't lack here is restaurants that happen to also be drinking establishments. Another that I'm fond of, closer to where I live (within stumbling distance) is Durty Nelly's, a dive bar in a deli (I told you; they're all restaurants). It, too, has been around even longer than I have, which is saying something. Hell, I first went there before it was technically legal for me to do so. (Hopefully the statute of limitations has expired by now.)

But there's one kind of place I know you've been waiting for me to talk about, Andre, and I'm going to wax poetic about them right now: craft breweries.

While there are no bars in Virginia, state law does grant an exception for sales of fermented beverages brewed on premise. While many breweries do feature food service -- some of it excellent -- others serve beer alone in flights and pints, or in bottles or cans for takeout, or both. Don't worry; they usually have pretzels or something on hand because the carbs in beer alone just don't cut it.

First, let's visit South Street. The oldest continually operating brewery in Charlottesville (there was an older one but they moved a few miles west a while ago), it features a wide variety of excellent brews and some delicious food.

A few blocks away stands a shining beacon on a hill: Random Row. Big place, indoor and outdoor seating, and if you get hungry, the best bagels in the state are just a short stagger away.

Keep going down that street, past Kardinal Hall (which is not a brewery, but a taphouse with a truly mind-boggling selection of beers from all over), in a run-down old garden shop building all of white-painted cinderblock, is Rockfish Brewing, which is a small-batch, no-nonsense paradise of a nanobrewery.

Near there is the satellite brewery of Starr Hill, which is the one that used to be in town, then moved out, then ironically opened this taproom just a few blocks from its historic home.

I'm not a fan of Starr Hill, but a lot of people seem to like it, so whatever.

Another one I'm not big on is Champion, way back over closer to South Street, but again, whatever floats your bananas.

Which brings us to my favorite brewery in Charlottesville (and my second favorite brewery in the whole country), located just above one of the few sake breweries in the US, a brewpub called Three Notch'd. The brewer there, Dave, is an artistic genius in his chosen medium (beer), and while I can't say I like every offering they have, there are some I'd rank right up there with the finest Belgians or established British styles. Their food is excellent, too.

There are a few more that are technically just outside of city limits, but are close enough so I count them: Decipher, run by former spies; Selvedge, near Decipher in the former Woolen Mills industrial building, a painfully hipster hangout; and Reason, on the north side of town, which makes a brilliant Russian Imperial Stout that's almost as good as Old Rasputin.

And here, I'm not even getting into all the distilleries, cideries, and wineries in the area. Most of them are out in the county, anyway.

Oh, while you're here, since you asked about famous sites, you might also take a trip to Monticello, a couple of miles outside of town. After all, Thomas Jefferson's greatest contribution to American society was his attempt to plant French grapes for making wine. They failed, but the idea stuck around and eventually, thanks to SCIENCE, came to... wait for it... fruition.

So, that's it: the tour of Things That Truly Matter in Charlottesville. If you survived, come back and drink us again!

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