Tag Archives: Art

New Release: Fractals – 2017 Adult Coloring Calendar

frontcover

I know how it is. You get to the end of November and you realize you forgot Mandelbrot’s birthday (it was Sunday). Or your friends ask you to come over for Pi day and then laugh at you when you bring pie instead (which they eat without thanking you). Well don’t worry, I’m looking out for you.

Introducing Fractals – 2017 Adult Coloring Calendar.

Did you know that you can make up math holidays just by choosing the right numbers? I mean, tomorrow is Fibonacci day because it’s 11/23 (it’ll really be cool in 42 years when it’s 11/23/58). I even made up my own holiday on January 26th: Koch curve day (because the approximate fractal dimension of the Koch curve is 1.26. It’s also E. H. Moore’s birthday apparently).

kochtricurve1l4

Feeling stressed? Why not color in some fractal bubbles or a cozy quilt? And take some time to marvel at the clean numbers and lines of the calendar template I created using a python script. There were definitely at least five tiny pixel adjustments to make sure the numbers lined up in diagonals just right.

Perfect for the math geek who also enjoys trivia and pretty colors. But even if your name isn’t Brian Buckley this calendar is a great for someone looking for something just a bit different in their date tracking this year. Available now on Amazon from the good people at Green Frog Publishing.

Advertisements

1 Comment

Filed under Books + Publishing

What I never expected

I’ve been off WordPress for a while and so it’s been a while since I checked my stats, and I was surprised to learn that I had something like a 200% increase in traffic last week, and for the best reason.

My “Fractals You Can Draw” posts have always been the most popular ones on the site. In general I think the writing life is weird like that. You never know what 20 minute or hour long effort is going to be the one that really lasts. I’ve spent hundreds of hours writing this blog, but that week I spent getting my wife to draw fractals, building a Sierpinski triangle out of marshmellows and toothpicks, and frantically trying to update by C++ skills has been one of the more lasting efforts of the last five years for me.

But the best thing is every year around the spring and fall I get new referrals from schools. WordPress does a pretty good job of letting you know where traffic is coming from, and every year I find some new class, ranging from grade school to college that references one of my fractal posts. That’s really the reason I’m doing any of this. What I’ve learned since I started blogging and especially in the last year working on the “Fractals You Can Draw” book is that I really want to teach people. I like writing fiction, but I love writing about math.

Honestly I’m as shocked as the rest of you.

Right now I’m working on Chapter 5 of the new book (or trying to, it’s been a crazy couple of weeks). I’m learning about new ways to use the Fibonacci sequence to draw fractals, and I can’t wait to share what I’ve learned. I’m so excited about this stuff I even snuck in a half an hour to write on Monday night while I was waiting for my mom to finish her grocery shopping.

If you’ve found this blog through one of your math courses I’d love to hear from you. To all the teachers who included links to my posts in their courses, thank you. And thank you for teaching people about fractals. It’s one of the best ways to build a love of math.

1 Comment

Filed under Writing, Writing Goals

Try as you go

I’m working on an expansion of Fractals You Can Draw transforming it from a pamphlet I wrote in the space of a week to something that could be used in a 6-9th grade math class. I want the book to serve not only as an introduction to fractals, but as a gateway to other interesting areas of math, and even world culture.

But at the core, the book still needs to be fun to draw.

I’m heavy in the research phase of this book and for the last few weeks I’ve been studying a traditional form of drawing native to Southern India (in the Tamil Nadu region) called Kolams.

KolamAttempts

Kolams have a lot to teach the casual math enthusiast or the serious math student about fractals, symmetry, context-free grammars, hexadecimal encoding and countless other subjects. They also can be kind of tricky to draw as you can see from my increasing lack of skill from top to bottom. All of these are theoretically able to be drawn free-hand as one long continuous line, but it takes practice.

I keep free-hand notes in part to test the difficulty level of what I’m expecting people to draw. Even in the original series I drew a couple of the images, and the little red-haired girl handled the other two, which gave us both a sense of how long it took to draw each image and some of the difficulties involved. I’d known how to draw all of the fractals in that series of posts for years, but it took actually trying to draw them by hand before I really knew how they worked.

What I’ve learned from drawing Kolams is that it takes a lighter, freer touch than is my natural inclination. And maybe gel-pens that smear easily aren’t the way to go either. You can make some pretty images very quickly, but you need to get a sense of the flow as you draw, or you can easily go off track (as I did multiple times on the bottom image).

More generally it is important for the writer to be able to take a step back and engage with whatever they’re writing as a their final target audience. Especially when you’re down the rabbit hole of research, it can be easy to lose a sense for how easy or difficult a particular subject is, and you need to take the occasional application step back. This is good not only for assessing the level of difficulty, but also in solidifying the theory behind what you’ve been studying. There were properties of how Kolams were drawn that didn’t gel in my head until I’d tried to draw a few.

You are your first beta reader. It’s still important to get outside perspectives, but trying things yourself helps you discern what should actually be included in the first place, and what should be left out. Engage with your work in different ways: read it aloud, read it out of order, try to actually follow your how-to directions without any outside info, color in your coloring book, etc. Whatever your genre, there’s more than one way to look at your book, and there’s value in gaining that new perspective.


You can read the original Fractals You Can Draw series here or check out my other book from Green Frog Publishing, Adult Coloring Book: Fractals (adultcoloringbookfractals.com) with cover art by the little red-haired girl.

FractalFacebookAdBlue

Leave a comment

Filed under Writing

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.

FractalAd10

1 Comment

Filed under Books + Publishing

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!

1 Comment

Filed under Uncategorized

Fractal Coloring Book – Cutting Room Floor

As I said yesterday, I produced over 100 images for the new coloring book, some of which were pretty cool but didn’t quite make the cut. Thought I’d share a few of my favorites for this long overdue “Fractal Friday.”

Have a great weekend!

Leave a comment

Filed under Uncategorized

Making a Fractal Coloring Book

FinalFrontCover

A lot of the projects I take on are just natural extensions of the things I immerse myself in (i.e obsess about). Even before being contacted by a publisher I’d been considering a fractal coloring book project for a little while. I had a lot of the programs I’d need, and 1000’s of images I’d generated in producing my previous two fractal books and subsequent posts. All I  would need to do is select the best of them, maybe write a good intro, and I’d have a quality book.

I think the only way we take on big projects is by deluding ourselves into thinking they’re not big projects, then plowing forward full steam ahead.

For a start, fractals that are good to color have a very different set of criterion from most of the fractals I’d been creating up to this point. You want something intricate but not so detailed that you can’t color it. You want some kind of pattern, but nothing too regular. You want something very open to interpretation, but with some common points of reference to give you guidance. You want a good variety of images, while providing people enough of what they’ll like. You need to cater to different difficulty levels, and because I like to teach about fractals as well, you need to use different generation techniques.

That’s a lot to think about when you’re trying to make 25 images.

Creating fractals for this book fell into one of a few different modes. There were a few, including the dragon curve and the Apollonian Recursive Gasket (see below), that were “classic” fractal designs that I felt just had to be in a book like this (though for the life of me I couldn’t get a Mandelbrot Set image I was happy with, maybe next book). In the case of the gasket, my insistence on including it might have had a little to do with spending 8 hours trying to write the code that would correctly generate the image (including learning a new way to think about circles, more on that some other time).

004_Bubbles (1-3)

Other designs were created by looking at things around me, a pattern on a quilt, a set of kitchen shelves, and playing around with some L-Systems interpretations of those objects until I got something I liked. Or other times I would draw out a small axiom on paper, sketch out a potential replacement rule, and just see what happened.

The third method involved perusing the thousands of Julia and L-System pictures I’d previously generated for my two fractal books and for posts on this site (this is where my new $50 kindle came in handy). The Julia images in particular took a lot of work, as the generation time to get an image with a good drawing edge is pretty long (2-8 hours on my quad-core laptop). L-Systems by comparison usually take at most only a few minutes, meaning you can experiment a lot more with tiny changes to see what the new result might be. This is probably why 19-20 of the images in the final text are variations on L-Systems and Turtle graphics.

Overall I produced well over a hundred images, culled from potential lists in the 1000’s. By comparison the selection process from those 100 was pretty simple: print the image out, run it by my wife to see if it’s a good candidate, and try not to make too many agonized screams when an image that took many hours to generate is rejected. Actually, my wife had a lot of good suggestions for potential ideas, or questions about tweaks I could do to make an image better.

The initial arrangement of the final images was done on my basement office floor, with one of us playing goalie to keep the dogs from walking all over the paper. Some things are just easier when you can see them out in front of you. We marked each image with a crayon indicating the rough level of difficulty, and moved sheets around until we got an arrangement we liked.

And this was all before I’d written a word.

Just to be clear, this was all great fun for me. I’ve seen other examples of coloring books where people slap together a bunch of stock images, or throw a bunch of their own previous work in without a lot of thought as to whether it would be fun to color. I didn’t want to make a book like that. I always like to create something new. Sure, there were times when I’d create 15 images and only get one good one, but that’s pretty much the experience with every creative endeavor. And there were plenty of “rejected” images that I had a new idea about, and made something even better.

This applies to just about any kind of writing. Writing something you later cut is never wasted effort. Everything is part of the process of making the final product, and even the things you look at and go “what was I thinking” had a part in shaping the final whole. And into making you a better writer or artist.

——————

My new book, Adult Coloring Book: Fractals is available now on Amazon. Published by Green Frog Publishing. You can see some of the fractals from the book, and color art by my wife (“the little red-haired girl”) on my new website bentrubefractals.com.

Leave a comment

Filed under Books + Publishing, Writing, Writing Goals