Tag Archives: Art

New Release – Adult Coloring Book: Fractals

So here’s what I’ve been up to the last couple of months…

FinalFrontCover

My latest book, Adult Coloring Book: Fractals, is available now on Amazon!

I’m excited to publishing this book with Green Frog Publishing, a small Indie Publisher based in Vermont. This book is actually the second in a series of coloring books, the first of which is a great set of hand-drawn images of the Adirondacks by Dave Campbell.

This book has been a real collaborative effort, including the proofreading talents of one Mr. Brian Buckley, cover and website art by my wife, and editing by Cecilia Bizzoco. Green Frog’s been just great, providing a lot of personal attention and developmental feedback to make this a better book than anything I could have done alone.

The Adult Coloring Book: Fractals is a collection of 25 fractal images for you to color and enjoy. Along the way you’ll learn the basics about fractals, and how some of the individual images were created. Most of this is all new material exclusive to this book (we’ll talk more later in the week about the production process). There’s also an extensive glossary with even more fractal explorations and resources (any glossary that includes a definition for the “Genesis Effect” is okay in my book).

I think fractals are uniquely suited to adult coloring books in that they offer a lot of freedom for interpretation. How you color these images is entirely up to you. Just seeing some of the work my wife put together really made these fractals come alive for me.

You can check out some of the images from this book on my new website BenTrubeFractals.com or buy the book from Amazon.com. Particularly check out the “Play with Fractals” tab for some of the unique L-Systems in this book.

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The Fractal Man (Axiom)

The third iteration (part) of my serial short story will be posted on Wednesday. For today as I sit here in my church listening to some live killer sax (from Molto Cappriccio) and waiting for 147 Windows 7 updates to install, I thought I’d give you a little background for this story, and to reassure some of you that most of it is fictional.

As with a lot of things here on the Blog, this short story is an experiment, a little bit of a departure from my regular genre to write a more introspective piece. My mom said this is a very “English major-y” story. I’m not sure what that means, but as a writer I like to think I can write any sort of genre, hopefully still with my own voice.

This much is true about the story you are reading, whenever I look at trees I see fractals.

It doesn’t quite rise to the level of affliction as with my character, but it is definitely a change in the way I perceive reality. Apparently spending a year and a half in deep study of the subject (and if we’re honest fairly continuous interest afterward) can cause the way you look at the world can change. I don’t know if this is permanent and it isn’t the same for every tree. We visited Jekyll Island for vacation a few weeks ago. There the trees are palm with Spanish moss growing all over them. Though I know they can be modeled with fractals, I haven’t yet studied the method deep enough, and it was somewhat calming to just see trees and not fractals.

I do sill love fractals, I wouldn’t be contemplating writing a second volume about them if I didn’t, but it is fascinating to observe how what you put in your head shapes you. If I had spent the last two years deep in revision in Dark Mater, or writing the next two Surrealities, no doubt my view point would be very different.

Another inspiration for this story is the book The Man Who Mistook His Wife For A Hat, a book containing narrative case studies of various mental afflictions. I found this book deeply fascinating, particularly the ways in which the patients perceive reality, or unreality, when certain parts of the brain are damaged.

As for why I’m writing this story there are a couple of additional reasons. I was a little geared up to write a story this weekend for the NYC Midnight contest, and though I sadly didn’t make it to the second round (though friend of the blog Jo Eberhardt did and hopefully her latest story went well), I wanted to have a place to spend that energy. And as far as process goes, this story is being written on the fly, in much the same fashion as Denied the Stars last year. I know where the story is going, and most of the component parts in the middle (I didn’t avoid going to Vegas just because I’ve never been there in real life, though this be madness and yet there is a method in it). Oh and I know trees aren’t dead in the winter, they lie dormant, but to my character they appear dead. Foreshadowing, or setting a tone ;). Each iteration is written the day before it is posted, usually in about in an hour.

So be sure to check out the first and second iterations before Wednesday. Hopefully you’ve enjoyed the story thus far, and where it is going. Feedback is definitely appreciated. I post stories like this here to learn what works and what doesn’t, so feel free to say anything. And feel free to ask any questions I haven’t covered here. You never know I might answer 😉

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A Fractal For Friday

I’ve been messing around with some new color algorithms, as well as complex trigonometric functions. I have a lot of pictures I want to show you, but for now we’ll just go with one of my favorites for the week:

FC_43B_c7

And yes, if there was ever any doubt, I’ll probably be writing a volume 2 of the fractal book, but I promise I’ll finish Surreality first.

Happy Friday!

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The Pi Day sale is live!

Head on over to bentrubewriter.bundledragon.com to get Fractals: A Programmer’s Approach and loads of exclusive content for as little as $2.99!

Pi Day Sale Ad Panoramic

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“Pi Day 5 Day Sale” Starts Tomorrow!

Tomorrow is Pi day, celebrating the number (and the tasty baked good). It’s a day to celebrate all things mathematical, so in that tradition I’m offering a 40% discount on the Fractals: A Programmer’s Approach bundle.

Pi Day Sale Ad 1 HD

This sale is exclusively on Bundle Dragon, and includes content you can’t get anywhere else.

For $2.99 you get Fractals: A Programmer’s Approach in Kindle, Nook and PDF formats (all DRM free), plus a high resolution gallery of 125 pictures from the book.

For just a dollar more you get the popular eBooklet Fractals You Can Draw, plus another gallery of 125 pictures not available anywhere else, and nearly an hour of fractal video exclusive to Bundle Dragon. That’s two books, 250 pictures, and dozens of fractal videos for just $3.99!

Pi Day Sale Ad Panoramic

But don’t delay, this sale only lasts until Tuesday 3/18*. Visit bentrubewriter.bundledragon.com for details.

*3.18 the first few digits of one of the early approximations of Pi, 7/22.

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Bonus Friday Post “First Fractals of the Year!”

For today’s post I thought I’d take you through some of my “creative process” for playing with L-Systems, fractals created using an algorithmic grammar.

We start with a simple shape:

StartingThought

This shape is my “replacement rule” for the L-System. To draw this shape I use the sequence of letters F-F+F+F-F, with F meaning “draw a line forward”, ‘-‘ meaning “turn left 120 degrees” and ‘+’ meaning “turn right 120 degrees.” If I start with a triangle, and replace each side of the triangle with this starting shape I get the following:

FirstStage

If I repeat this for each line of the new shape, and again on each line of the resulting shape, after a few iterations I get this:

SierGasketInnardsLSys_LQ

The Sierpinski Gasket, one of the most persistent recurring fractals with untold methods for drawing it.

But what if I didn’t start with a triangle? What if I started with a square?

Then I’d get this:

SierGasketChineseStarLSys_LQ

That’s pretty good, but if what if inverted the square by flipping it inside out. A typical square is drawn F+F+F+F with ‘+’ being a right turn of 90 degrees. But if I change those pluses to minuses I get this:

SierGasketChineseStarInvertLSys_LQ

And here’s what an inverted pentagon would look like:

SierGasketPentagonInvertLSys_LQ

Okay, that’s pretty good, but what if we skewed our initial replacement shape?

FirstSkew

So now our initial triangle would look something like this:

FirstSkewStage

Keep repeating this process and you get something really different:

SierGasketInnardsSkewedLSys_LQ

Same number of lines that we used to draw our Sierpinski Gasket, but with less overlap (this is one of my favorites). Let’s try another skewed shape:

SecondSkew

And the resulting first stage is:

FirstSkew2Stage

Now what do we get?

SierGasketInnardsSkewed2LSys_LQ

That’s good but let’s invert it. Our first stage is:

Skew2Inverted_Skew3

And after a few iterations we get:

SierGasketInnardsSkewed3LSys_LQ

Now let’s start with an inverted hexagon:

Skew2InvertedHex_Skew4

And see what happens:

SierGasketInnardsSkewed4LSys_LQ

If we turn the hexagon right-side out:

Skew2Hex_Skew5

We get this:

SierGasketInnardsSkewed5LSys_LQ

But L-Systems also allow for moving without drawing a line, typically represented by the ‘f’ character. Let’s take our first motif and remove a section:

FirstSkip

If we apply this replacement rule to an inverted triangle we get this:

FirstSkipInvertedFirstStage

And after a few iterations:

SierGasketInnardsSkipLSys_LQ

Turn our triangle right-side out and we get:

FirstSkip_Skip2

Followed by:

SierGasketInnardsSkip2LSys_LQ

Here’s a couple other skip motifs:

SierGasketInnardsSkip3LSys

And the result:

SierGasketInnardsSkip3LSys_LQ

Initial Stage:

SierGasketInnardsSkip4LSys

Result:

SierGasketInnardsSkip4LSys_LQ

Now let’s remove some sections from our skewed replacement rules:

SierGasketInnardsSkewedSkipLSys

First Stage:

SierGasketInnardsSkewedSkipLSysFirstStage

Result:

SierGasketInnardsSkewedSkipLSys_LQ

Replacement Motif:

SierGasketInnardsSkewed2SkipLSys

First Stage:

SierGasketInnardsSkewed2SkipLSysFirstStage

Result:

SierGasketInnardsSkewed2SkipLSys_LQ

Each of the above shapes had no replacement rule for ‘f’ so these segments were kept empty. If we use the same replacement rule for ‘f’ as we do for ‘F’, we get these respectively:

SierGasketInnardsSkewedSkip2LSys_LQ

And this:

SierGasketInnardsSkewed2Skip2LSys_LQ

Similar to our originals, but with less internal lines.

Finally, let’s look at a couple more variations. A wider initial stage can stretch our gasket:

Motif:

SierGasketInnardsWiderLSys

First Stage:

SierGasketInnardsWiderLSysFirstStage

Result:

SierGasketInnardsWiderLSys_LQ

And a hex-bump creates a non-overlapping curve.

Motif:

HexagonBumpLSys

First Stage:

HexagonBumpLSysFirstStage

Result:

HexagonBumpLSys_LQ

All of these shapes were created from variations on a five-line motif. Hopefully you can see from this post how tiny variations in method can create huge changes in result.

Have a happy fractal friday!

*All images were created using L-System 6 from Chapter 4 of Fractals: A Programmer’s Approach available on Amazon. Download a docx file containing all of the XML data for these images here. Hi-res versions of the above images are available by clicking on each image.

Like cool fractal designs, maybe some you can color? Then check out my latest Adult Coloring Book: Fractals available on Amazon.

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Fractal Friday “Grayscale Friday”

I’ve been experimenting with some black and white fractalizing, using a couple of new grayscale and inverted grayscale color filters on my Mandelbrot program. Here are some of the very preliminary results:

BOF_Map45_gs_r

FB_Mandel_(0.3911)_(0.229471)_00442_widebsm_gs_r

The inverted grayscales are the ones with white Mandelbrot sets.

BOF_Map48_gsi_2

FB_Mandel_Claw_01920church_bw_gs_r

FB_Mandel_(0.3911)_(0.229471)_00442_widebsm_gsi_r

BOF_Map48_gs_2

Happy Friday!

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