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Monday, Jun. 3, 2024

8:18am EDT

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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

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Show Recent Comments

10 Most Recent Blog Comments:

Elisa the Bunny Stik

about 21 hours ago
In response to "Revisited: "Nonbinary""

"We desperately need "accept yourself as you are" messages, but there's no money in that"

Tell that to Psychology Instagram influncer types. They'll be willing to sell services that help you accept you as you are.

Elisa the Bunny Stik

May 29, 2024 at 9:02am
In response to "Ordinary Average Guy"

I think we need to be careful about saying there's no difference in socializing between online and off. I saw the following in response to a comment about discussions of gender online and the stances taken by LGBTQ community members that are chronically online:

"Truth. I had to stop looking for queer spaces online because it was full of this and angry exclusion discourse. I found some queer spaces offline and it reminded me that most people are normal and chill."

This is a topic I will likely be visiting in my journal in July. I figured I'd at least get this response in here first as a warm-up.

1 Like

Elisa the Bunny Stik

May 28, 2024 at 1:46pm
In response to "Long in the Tooth"

I feel I was too busy as a teen to screw around in convenience stores. On the rare occasion I wasn't at school or working, I tended to hang out by myself. If I hung out with friends, it was usually at someone's house (rarely mine).

Elisa the Bunny Stik

May 27, 2024 at 11:42am
In response to "Olive It And More"

Every once in a while, someone will misread the order slip and give me green peppers, which are an abomination, instead of green olives.

They truly are an abomination. If you're going to put peppers on a pizza, make sure it's anything but those little soggy cardboard slice things. Hell, even poblanos would be a major upgrade.

1 Like

Elisa the Bunny Stik

May 27, 2024 at 11:38am
In response to "Coming Up the Pike"

Man, people on Fandom Secrets would be aghast at how much you like Strange New Worlds. Personally, I haven't seen much of it. However, I did watch an episode at the gym once and found it enjoyable. It gave me that fascinated feeling I had when watching The Next Generation as a kid.

1 Like

Elisa the Bunny Stik

May 27, 2024 at 11:13am
In response to "Burgundy"

I will admit that I'm not much of a wine drinker. I've had reds and whites but tend to prefer reds. Then again, when it comes to booze, I tend to prefer things that are more intense in flavor. White wines...tend not to be that way for me.

2 Like

Elisa the Bunny Stik

May 27, 2024 at 10:38am
In response to "Distrust the Process"

That being said, I do think that people going out of their way to demonize ultra-processed foods are causing just as many issues as lobbyists are. These folks' actions exacerbate eating disorders and nervous thinking around food insecurity in equal measure. I wish the conversation around this set of actions was louder.

3 Like

Elycia Lee ☮

May 27, 2024 at 10:31am
In response to "Distrust the Process"

To me, as long food is 100% natural, then it is healthy. Pretty much like fruits, veggies and rice. I know people have thoughts about whether rice is good or not, but it is natural food so... I shall go with that.

2 Like

Kåre Enga in Montana

May 25, 2024 at 3:13pm
In response to "Plan Solo"

I'm more introverted than extroverted, but my only apprehension involves language and cultural barriers.

I'm bi- or ambi- but... always annoying. I waver between wanting to be left alone and not wanting to be alone.

I make my adjustments as necessary.

But LANGUAGE and CULTURE: true barriers that can cause problems for some and angst for me. I love strangers but find it frustrating when I can't connect.

For Belgium: make those plans soon. Today's connectivity means booking lodging in advance. In the old days it was show-up-and-ask-if-they-have-a-room. Still possible but not recommended unless cost is not an issue.

I prefer staying in hostels but rarely join in 'events'. I have gone out with fellow travelers however.

Kåre Enga in Montana

May 25, 2024 at 2:58pm
In response to "Banned Camp"

I remember when the movie "Brokeback Mountain" received "F"s from folks who basically commented that they would never NEVER watch such filth. Even those who liked or enjoyed it missed the main theme of poverty (financial, cultural, individual...). Personally, I preferred the short story to the movie. Both made a point that America didn't/doesn't want to face: choice and lack of choice.

That said, if someone were to ban my poetry I could probably live off of the notoriety.

Burning at the stake though seems a more likely outcome.

2 Like

#1816. In The Name Of Name
ID #1023220 entered on December 15, 2021 at 12:01am

#1815. A Gift Beyond Price, Almost Free
ID #1023186 entered on December 14, 2021 at 12:03am

#1814. Congratulations!
ID #1023146 entered on December 13, 2021 at 12:02am

#1813. Two Years
ID #1023096 entered on December 12, 2021 at 12:08am

#1812. Weekness
ID #1023061 entered on December 11, 2021 at 12:02am

#1811. Too Little, Too Late
ID #1023024 entered on December 10, 2021 at 12:06am

#1810. In Spite Of
ID #1022986 entered on December 9, 2021 at 12:02am

#1809. Transcendental
ID #1022945 entered on December 8, 2021 at 12:03am

#1808. Meh. Whatever.
ID #1022904 entered on December 7, 2021 at 12:02am

#1807. Astronomically
ID #1022813 entered on December 6, 2021 at 12:05am

#1806. Dinostory
ID #1022774 entered on December 5, 2021 at 12:02am

#1805. It's A Conspiracy!
ID #1022750 entered on December 4, 2021 at 12:01am

#1804. Know One
ID #1022713 entered on December 3, 2021 at 12:04am

#1803. How Low Can You Go?
ID #1022679 entered on December 2, 2021 at 12:51am

#1802. You Have Nothing to Lose But Your Chains
ID #1022595 entered on December 1, 2021 at 12:01am

#1801. Try to November Me
ID #1022544 entered on November 30, 2021 at 12:03am

#1800. Future Perfect
ID #1022488 entered on November 29, 2021 at 12:02am

#1799. Life, The Universe, and Everything
ID #1022439 entered on November 28, 2021 at 12:01am

#1798. Go Home
ID #1022387 entered on November 27, 2021 at 12:02am

#1797. Busted
ID #1022331 entered on November 26, 2021 at 12:02am

#1796. Putting the Attitude Back in Gratitude
ID #1022273 entered on November 25, 2021 at 12:02am

#1795. I Did Nazi That
ID #1022227 entered on November 24, 2021 at 12:03am

#1794. Gelotology
ID #1022175 entered on November 23, 2021 at 12:01am

#1793. Powered Up
ID #1022096 entered on November 22, 2021 at 12:01am

#1792. Facing the Music
ID #1022046 entered on November 21, 2021 at 12:03am

#1791. People Eating Tasty Animals
ID #1021994 entered on November 20, 2021 at 12:01am

#1790. Epiphany
ID #1021917 entered on November 19, 2021 at 12:04am

#1789. Experience
ID #1021842 entered on November 18, 2021 at 12:01am

#1788. The Butler Did It
ID #1021786 entered on November 17, 2021 at 12:09am

#1787. Thought for Food
ID #1021729 entered on November 16, 2021 at 12:04am

#1786. Dark Side of the Moon
ID #1021645 entered on November 15, 2021 at 12:04am

#1785. Past Tense
ID #1021569 entered on November 14, 2021 at 12:02am

#1784. Procreation Pass
ID #1021510 entered on November 13, 2021 at 12:03am

#1783. Avoidance
ID #1021438 entered on November 12, 2021 at 12:02am

#1782. Nothing to Go On
ID #1021370 entered on November 11, 2021 at 12:01am

#1781. Hay Now
ID #1021286 entered on November 10, 2021 at 12:03am

#1780. Barber-ians at the Gate
ID #1021211 entered on November 9, 2021 at 12:02am

#1779. Decade Dance
ID #1021118 entered on November 8, 2021 at 12:02am

#1778. The Einstein Trap
ID #1021039 entered on November 7, 2021 at 12:05am

#1777. A Productive Day
ID #1020958 entered on November 6, 2021 at 12:04am

#1776. Solutions
ID #1020862 entered on November 5, 2021 at 12:10am

#1775. Hide-And-Seek Champions
ID #1020795 entered on November 4, 2021 at 9:10am

#1774. Tourist Trap
ID #1020692 entered on November 3, 2021 at 12:01am

#1773. Beer Necessities
ID #1020605 entered on November 2, 2021 at 12:01am

#1772. Bare Necessities
ID #1020504 entered on November 1, 2021 at 10:25am

#1771. Not in De Nile
ID #1020458 entered on October 31, 2021 at 12:03am

#1770. Scare Tactics
ID #1020407 entered on October 30, 2021 at 12:02am

#1769. Squash Court
ID #1020340 entered on October 29, 2021 at 12:02am

#1768. We'll See Who's the Total Moron
ID #1020279 entered on October 28, 2021 at 12:03am

#1767. The Play's the Thing
ID #1020216 entered on October 27, 2021 at 12:01am

#1766. What Do You Mean, "Leftover Pizza?"
ID #1020145 entered on October 26, 2021 at 12:04am

#1765. Fonio
ID #1020062 entered on October 25, 2021 at 12:01am

#1764. Hardly Working
ID #1020012 entered on October 24, 2021 at 12:03am

#1763. Birth of a Spaceship
ID #1019922 entered on October 23, 2021 at 12:01am

#1762. Productivity
ID #1019807 entered on October 22, 2021 at 12:02am

#1761. Sushi
ID #1019759 entered on October 21, 2021 at 12:07am

#1760. Tragedy
ID #1019687 entered on October 20, 2021 at 12:03am

#1759. Man
ID #1019641 entered on October 19, 2021 at 12:03am

#1758. Speling Iz Dificult
ID #1019575 entered on October 18, 2021 at 12:03am

#1757. Allez Cuisine
ID #1019515 entered on October 20, 2021 at 10:30pm

#1756. We're All Mad Here
ID #1019445 entered on October 16, 2021 at 12:02am

#1755. How the Bible Can Lead You Astray
ID #1019364 entered on October 15, 2021 at 12:06am

#1754. In a Jam
ID #1019301 entered on October 14, 2021 at 12:02am

#1753. Meat the Press
ID #1019239 entered on October 13, 2021 at 12:01am

#1752. The End
ID #1019158 entered on October 12, 2021 at 12:03am

#1751. Bubble Rap
ID #1019101 entered on October 11, 2021 at 12:08am

#1750. There's No Ham in Hamburger
ID #1019041 entered on October 10, 2021 at 12:04am

#1749. The Sioux Chef
ID #1018996 entered on October 9, 2021 at 12:13am

#1748. Trivial Pursuit
ID #1018914 entered on October 8, 2021 at 12:01am

#1747. Personality
ID #1018859 entered on October 7, 2021 at 12:01am

#1746. Evil Genius
ID #1018774 entered on October 6, 2021 at 12:02am

#1745. Lyin's Mane
ID #1018723 entered on October 5, 2021 at 12:02am

#1744. Inventive
ID #1018650 entered on October 4, 2021 at 12:02am

#1743. Irrational Primacy Effect
ID #1018576 entered on October 3, 2021 at 12:03am

#1742. I Will Get My Revenge
ID #1018506 entered on October 2, 2021 at 12:02am

#1741. Praise Cheeses!
ID #1018454 entered on October 1, 2021 at 12:03am

#1740. Wake Up Now
ID #1018365 entered on September 30, 2021 at 12:03am

#1739. Han Shot First
ID #1018245 entered on September 29, 2021 at 12:03am

#1738. To Sleep, Perchance To Demon
ID #1018177 entered on September 28, 2021 at 12:01am

#1737. Speculation
ID #1018112 entered on September 27, 2021 at 12:02am

#1736. What Culture Now?
ID #1018060 entered on September 26, 2021 at 12:01am

#1735. Happy Mead-ium
ID #1018010 entered on September 25, 2021 at 12:01am

#1734. Hard, Erect Deck
ID #1017962 entered on September 24, 2021 at 8:32am

#1733. Friend
ID #1017903 entered on September 23, 2021 at 12:01am

#1732. Out There
ID #1017850 entered on September 22, 2021 at 12:12am

#1731. We Got The Beat
ID #1017797 entered on September 21, 2021 at 12:01am

#1730. Ten
ID #1017739 entered on September 20, 2021 at 12:02am

#1729. The Thinkers
ID #1017695 entered on September 19, 2021 at 12:02am

#1728. Irregardless
ID #1017641 entered on September 18, 2021 at 8:21am

#1727. ...iiiiiiiin Spaaaaaace!
ID #1017585 entered on September 17, 2021 at 12:02am

#1726. Hyperlocal
ID #1017490 entered on September 16, 2021 at 12:03am

#1725. Uh huh. Sure.
ID #1017439 entered on September 15, 2021 at 12:03am

#1724. This Isn't Nam - There Are Rules!
ID #1017367 entered on September 14, 2021 at 12:02am

#1723. Past Lies
ID #1017312 entered on September 13, 2021 at 12:01am

#1722. The Game of Risk
ID #1017268 entered on September 12, 2021 at 12:06am

#1721. Drawing Conclusions
ID #1017222 entered on September 11, 2021 at 12:02am

#1720. Rhetorical
ID #1017159 entered on September 10, 2021 at 12:05am

#1719. Fight The Power
ID #1017070 entered on September 9, 2021 at 12:03am

#1718. The Screen Door Slams
ID #1017010 entered on September 8, 2021 at 12:02am

#1717. My Baloney Has a First Name...
ID #1016946 entered on September 7, 2021 at 12:03am

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