Tag Archives: fractals

Making an Adult Coloring Book: Kitchen Shelves

A number of the images in my fractal adult coloring book came from looking at objects around me. This is a set of shelves in my parent’s kitchen:

KitchenShelves

Understanding and creating new fractals means breaking shapes down to their most essential features. For L-Systems, which make up the majority of the images in my book, we call these essential features the axiom, or base image. The shelves are made up of five sections, a larger center section, and four small squares connected on each side. You might think the most essential feature is the whole shelf, but actually the most basic shape is a single square:

ShelvingKitchenL1

For simplicity, I made the shelves equal on all sides, rather than using rectangles of different widths, but the basic principle is the same. The above square is the axiom of our L-System. With each iteration (stage), we add four squares to each side of the square(s) from the previous stage. If we add a smaller square to each side of this base image, we get something resembling the kitchen shelves:

ShelvingKitchenL2

Not a bad model, but not very interesting to color yet. So let’s add four new smaller squares to each side of the four squares we added:

ShelvingKitchenL3

This is getting better. Already we can see how adding smaller squares creates interesting overlapping sections. At this stage we added 16 new squares, so let’s add 64 new squares to the next level (four on each side of the 16 squares we added):

ShelvingKitchenL4

And so on:

ShelvingKitchenL5

The level of intricacy used for a final image has to balance the expected medium (colored pencils and gel pens) with the ability to create many different types of patterns. The above stage is the one used in the book, but when using a computer to color, we can go to even higher levels of detail:

021_Little Boxes (1)

The above image was colored by my wife, who consulted with me on the best images to select for the book, and suggested their level of difficulty.

Creating new fractals is about seeing the potential for art all around you, even in the most basic and mundane parts of our lives. Simple patterns can be expanded into something intricate and beautiful. And deciding how to color these new patterns adds an even greater level of artistic expression. A simple object can be transformed into a universe of variations. That’s what I enjoy most about creating the coloring book, seeing how others take a pattern and make it their own.


If you enjoyed this post and would like to learn more about fractals, check out my Adult Coloring Book: Fractals available on Amazon.

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How long does it take you to buy a book?

flea-market-237460_1280

This will come as a surprise to exactly no one but I have a big fractal book wish list. I’ve actually become kind of obsessive about it since I’ve been focusing more on a specialized area of fractals, while still considering options for broader fractal surveys.

Back when I was writing A Programmer’s Approach, my method for selecting books was simple. Search “fractal” in Amazon. Buy any book that looked vaguely helpful and that cost $0.01 (+ $3.99 shipping). Of course even then there were special books that I would pay a little extra for, but overall I was looking for a broad survey of authors and perspectives.

Considering that I have a full bookshelf now of fractal books, and that the bookshelf has started to bleed over onto my desk, I do not need more general books.

But, and again this might surprise you, specialized books are expensive. A lot of the better fractal books fall into one of two categories: college textbook or obscure lecture notes from a math conference. In college spending $120 on a textbook was a necessary evil. In later life, especially one that expects it to take a while to make $120 from a fractal book, that price is a little steep.

I’ve started to camp on books, throwing their Amazon listing into a wishlist called the “buying queue” and I’ve noticed something weird. Usually, even an expensive book, will have two sellers who have the lowest price. These two prices will leapfrog each other down by a few pennies several times a day. It can sometimes take weeks of waiting, but you can knock a couple of bucks off the book’s price if you wait long enough.

However, if you wait too long and somebody snatches one cheap copy up, the other cheap copy shoots up in price to match the second lowest price, and they fight it out again. I’ve observed this behavior on comic books, DVD’s, regular books, etc. I’m pretty sure it must be a setting in the Amazon Marketplace, coupled with an algorithm. Either that, or all marketplace sellers are exhibiting the same behavior.

With the buying queue, a good five minute segment of my day is looking at a book, gleaning as much information as I can from the preview or the reviews, and deciding if this is the day I will buy it, or if it’s the day I decide to take it off my list entirely, or bump it down to a secondary wish list I check less often. I’ve had books I’ve debated over for months, doing the online equivalent of picking it up, flipping through the pages, and putting it back down again.

With reference materials in particular I want as little overlap as possible, while still getting something that builds on other material I have. I prefer electronic books just because I will read them more often, but still acknowledge that there’s nothing like flipping through a real book. I have limited shelf space, but I’m always willing to clear away the chaff for something great. And, probably most difficult, all of these books aren’t popular, so there’s virtually no reviews or sales rank to give me a sense of whether it is actually good. Occasionally I can find an academic review if I do some digging, but that only sometimes helps.

Do you think it’s too late to start a Kickstarter campaign so I can buy more books. I’d do it for my Star Trek comics as well, but I have a hard enough time convincing others that reading comic books is “research.”

Ah well. Maybe I’ll go to an actual bookshop this weekend and stare at those books for a while. Happy Friday all.

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Research Mode

Image Source: Tumblr

Image Source: Tumblr

I just got my first interlibrary loan yesterday (ILL for all you bibliotheque nerds). It is an interesting mix of adult responsibilities and genuine excitement. The book is due on April 30th (no renewals), and I will be fined $2.50 a day if it is not returned. There’s an envelope it must be returned inside, and a sleeve that is stuck to the outside cover. The cheapest I could have bought this book was $20, with most copies ranging more in the $50-$60 range. As I continue on the journey from a general interest in fractals to a more specialized exploration, there are only going to be more such books and loans (though I still have to fight off the hoarders mentality that I’d have if I had a University Library’s budget).

It struck me the other day how different the way I conduct research now was from when I was in highschool and college. The internet was a strong resource in both times, but where I’d be printing off papers in college and compiling them in a notebook, now I am just throwing things on my tablet. I found a 2000 page math encyclopedia on the Internet Archive the other day, and I can carry it around in my bag without any back strain.

Yet I still find myself working with paper when it comes to taking notes and working things out. Part of this is simply mobility, it’s easier to take notes on paper at idle moments than it is to use a computer. And part of it is that I believe as many do, that taking notes on paper is a better way to retain information and to organize thoughts. Plus it’s a way to make use of the dozens of notebooks that have piled up in my house that have yet to be filled with brilliant short stories.

I’m a little more specialized with these notebooks than college. I got into a genuine discussion with Brian over whether Moleskine is pronounced “Moleskin” or “Moleskeen” (I prefer the later even though it is likely wrong). And I have all different sizes, larger stay at home notebooks for rough work, smaller reporter pads for technical notes, and mid-size for more general information. My “go bag” has a tablet, an eReader and six notebooks!

And even when I find myself frustrated with pay-walls for articles, or expensive books, I am amazed at how much knowledge is just out there for free. Even with the potential for steep fines, getting a book from an inter-library loan was cheaper and almost as quick (if not faster) than buying the book myself. I do admit to some impatience with having to wait for physical materials, both waiting for them to arrive, and waiting for time to read them at home. It’s why I’m a fan of writing affordable eBook reference materials. But sometimes there’s nothing like a good primary source from an author whose name you need a pronunciation guide for.

How do you do research? Are you still a pencil and physical book sort of person, or is Google the way to all knowledge?

————

One of the results of previous research projects was Fractals: A Programmer’s Approach. If you’re looking for a gateway to understanding fractals, particularly how to make them, it’s not a bad place to start, and it’s free on Kindle Unlimited.

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Flowsnake

Not much time for a post today, so thought I’d share something I was working on last night:

GosperPlusPeanoGosper_blue

Kind of an old fractal classic, known colloquially as “Flowsnake” when it was written about by Martin Gardner, and also as the Peano-Gosper curve. The gosper curve at the border bounds the inner fractal so we can get the nice blue dye effect. I did this with a single L-System so I can generate all different sizes of the two curves, while still keeping them inside each other. Enjoy!

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Author Enters Rehab For Fractal Addiction

Ben Trube, author and one-time CMT background audience member, has admitted himself into the Helge von Koch Fractal Addiction treatment center earlier this week, following an incident that nearly resulted in the destruction of his home.

“I’m doing this for my family,” Trube said in a short statement.

According to reports, Trube had been working on a new technique for visualizing the Mandelbrot set when his laptop caught fire, destroying many treasured chotskies including a Pikachu made of Legos and a Snoopy stuffed animal.

“I’ve learned a lot about loss since that fire,” Trube added.

Trube’s addiction reportedly began sometime in late elementary school, with occasional math outbursts in his mid-teens.

“We’d walk down the hallway and suddenly there would be dozens of Sierpinski Triangles plastered all over the walls,” reported a former WKHS administrator. “Sometimes it took hours to pull those staples out of the corkboard.”

“I thought he’d left it all behind in college,” Trube’s wife stated when reached for comment. “But then he got the idea to write a book, and that brought it all flooding back.”

Soon the Trube home was buried in books by Saupe, Wolfram, and Devaney. In the months that followed, Trube reportedly sank dozens of dollars into any penny book he could find on Amazon.

“He’d light up when he found one with a floppy [disk] in the back,” Trube’s wife reported.

Sales of the new fractal book allegedly only served to deepen the author’s obsessive behavior.

“It became all he’d talk about at night. I’d be trying to go to bed, and all he’d want to talk about is L-Systems or some new Indian Kolam he’d discovered,” Mrs. Trube lamented.

An unnamed source within the Koch center reported that treatment has not been going well.

“He got a hold of a pencil and started drawing a dragon curve on his wall. When we tried to restrain [Trube] he started shouting ‘Z-two is Z-one squared plus c‘!”

Promotional Poster drawn by Trube for non-existent fractal MMA match.

Promotional Poster for non-existent fractal MMA match.

Nationwide, fractal addiction is the leading cause of death among mathematicians aged 80-100.

“Dr. Mandelbrot has a non-zero amount of blood on his hands.”

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Fractal Videos from the Coloring Book

I produced some new animations for the Adult Coloring Book showing how three of the images are drawn line-by-line. Several of these are variations on classic fractals, while “Cog in the Machine” is my own original creation. Enjoy!

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Waste of Time

I spent a good chunk of my weekend purging books, CD’s, computer games, console games, board games, and DVD’s from my life. The stated purpose of this latest purge was to raise some funds for a new fractal book I wanted to buy, and also the more general goal of weeding out the things in my life (and house) that are taking up space.

This is a task I meet with equal parts enthusiasm and grouchiness. I like clearing out new spaces in my office, getting clutter off desks, making it so less of my books have to be stacked on top of each other in my shelves, etc. I even get a certain good feeling from giving myself permission not to read something I thought I should back in the day.

But the task takes up a lot of time. I have media on all three floors of the house, and particularly in my office, shoved into just about every nook and cranny. To save space in my operational life, I keep the empty cardboard boxes for PC games (yes, we used to have those before there was such a thing as Steam) back in my storage area. At the moment the storage area cannot be walked into without moving a bunch of objects, and balancing awkwardly on one foot, but if I’m selling a game I want to get rid of its accompanying box.

And there are decisions to be made. I’ve gotten rid of things in the past that I’ve later regretted and re-bought. That is a waste of both time and money. Usually the two year rule works well for me. If I haven’t touched this in two years, it’s a potential for the chopping block, though there are lots of things that meet those conditions that still get a free pass.

Long story short I spent most of Friday, and a good portion of Saturday morning on this task, and earned $44 (about half of which was for the console games which took all of about five minutes to go through).

And then I determined that I didn’t want to buy the book that had kicked off this whole process in the first place.

OK, in the long run it wasn’t so bad. I got double fuel points for the Amazon gift card. After a couple of hours more weeding down my Fractal Book wish list, I did get a new book on L-systems that’s on its way, with budget left over for more. And I didn’t waste $36.80 on a book that wouldn’t have helped me much. Plus I gained a lot of space, though you’d hardly know it by looking.

I get frustrated at such expenditures of time because I would rather be spending my time creating new things. And it forces me to grapple with the fact that at varying times in my life I just let a lot of junk pile up, and now I’m trying to sift through it to determine if it has any meager value for the future. And these projects are always the sort of thing that start as a small project, and spin out into something that takes half the weekend.

I know that tasks like this are good in the long run. There’s a difference between busy work, procrastination, and actually organizing one’s life. And I got money from stuff that was sitting around gathering dust. Plus gathering research materials is a part of working on a book, even though it doesn’t feel like much. This is why authors should never figure out their hourly rate for creating a book. It would depress you to no end.

My wife says I should not let these things bother me, that the clearing away of junk is valuable in its own right, and of course she’s right. I spend a lot of time doing things that aren’t working on my book, and it isn’t all wasted time. In fact most of it are the parts of life that bring me the most joy. I wouldn’t have much to write about if all I did was work and sleep.

Now I just have to figure out how not to be such a grouch about it.

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