Category Archives: Writing

The writing life, tips, tricks, foibles, pitfalls and experience from one author’s perspective.

by Ben Trube | July 30, 2022 · 3:14 PM

On the way to Helsinki

I’m on my way to the Bridges 2022 conference in Helsinki, Finland. It has been… *checks watch*… five years since the last time I posted to this blog. I won’t try to catch you up in a single blog post on everything that’s happened in those five years, but suffice it say, the more things change, the more they stay the same.

At the moment I am sitting in the Chicago airport next to my friend Brian, on my way to present my first paper at a math conference. You can read it here, and as you can see I’m still writing about fractals. This will be my first trip overseas, and only my 3rd country overall (though we plan to add Estonia as well after the main conference).

The paper like many things is evidence that the only way to accomplish anything is to not know how much time it is really going to take you in the first place. These 4 pages (about 1200 words) are the culmination of some initial explorations two years ago, dozens of hours programming, 10’s of hours writing, some copy-editing from the aforementioned Brian, two rounds of reviews and revisions, 20 hours building a 3D model (for one picture) by hand, and another dozen hours or so writing a presentation (which I was revising for a few more hours before leaving the house yesterday). I’m excited, nervous, but I think generally ready, and even after I just gave you that laundry list, I want to do it all over again as soon as I can.

***The aforementioned 3D model, made out of PixBrix.***

The Bridges conference is really special. When I went there five years ago, I felt like I had met my tribe. I like working as a professional software engineer / architect, but it’s math and making art that excites me, and the opportunity to try to inspire that joy in others. The last time I went I felt like I learned more than I could take in all at once, and I’ve been itching to go back and learn even more.

I’m not sure when you’ll hear from me next. I am trying to scare together time outside my job to work on another programming book (this one in python/cython), but that could be quite a ways off. Going to the conference did at least drag me onto Instagram (https://www.instagram.com/fractal_man2147/). I’ll try to keep up with posting new artwork in-between larger projects. I may take a crack at other papers as well (maybe a longer paper for Bridges, or something for the Journal of Mathematics and the Arts). And I’ve got a pipe dream idea for a recreational mathematics magazine of my own. Maybe someday.

In the meantime, below is one of my favorite sandpiles from the work on the paper. It’s made using a quilting pattern called “Road to Oklahoma” and was color-sampled from the flowers in my garden.

Until we meet again, hopefully a little sooner next time!

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.

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Filed under Writing, Writing Goals

Tagged as Art, fractals, Math, School, Writing

by Ben Trube | August 8, 2016 · 12:05 PM

Dispatches from writing a new fractal book

I spent a lot of the weekend making figures. If a picture is worth 1000 words, then my book would be 500,000 words long. There are a lot of things to consider when making an image for a book:

Since this will be a B&W book, what’s the best gray-scale values to look two-tone without looking faded?
What resolution will work best for the print size, but still work for an eBook (so I don’t have to make two of every picture, hopefully)?
How does the image flow with the text? Does it make it hard to read, or does it illuminate a point the text is making?

This last is the primary goal of pictures. Pictures serve two purposes in my book: to show people pretty images, and to show people how to make pretty images. A lot of the heavier math texts I read can still be very informative if they have good illustrations that make it clear what the writer is trying to say. Still, you don’t want to lean on the pictures too heavily, the text still has to make sense.

My early drafting process has been to write the chapter without illustrations. I insert an [ILLUSTRATE] tag into my text where I think an image would/should go, and then I move on. So far this seems to be working okay. I’m remembering from writing the first fractal book that what I think is a clear explanation and image isn’t always what people actually understand, so I may have to try a few different images, and change the text accordingly.

It probably doesn’t make sense to talk this long about pictures without showing you one, so here is a Minkowski sausage:

Neat, huh?

One other weird quirk of the early going is the feeling that I’ve written this all before. In some ways, this fractal book is the culmination of 5-10 years of thinking about fractals, as well as an intense period of six months research. I have run through the progression of thoughts that make up the first chapters dozens of times in my head, and even though this one of the first times I’m committing them to paper in this particular order, it still feels like something I’ve been doing all along. Probably some of that comes from blogging about fractals, that’s really where this recent and previous interest started.

Last thought of the day is a nice little moment at the library. I was checking out yet another fractal reference, and got to talking with the librarian about the new book, and how I got interested in fractals back in the 6th grade EPP program at school (more than 18 years ago now). Turns out, her son had just recently been part of the same program, and had loved fractals and all of the ways you could use them to make math beautiful. It’s for these kinds of kids and curious adults that I’m writing this book, and it was a nice little encouragement to know that they’re still out there.

Have a good week. I’ll check in when I can.

Sharing someone else’s culture

I spent part of the weekend reading about creation myths and fables of the Chokwe, an ethnic group that lives roughly in Angola. This is part of my research for the new book, which is expanding to have an extensive “Ethno-mathematics” section (i.e. Math and Fractal Drawings from around the world), specifically the Chokwe tradition of Sona. Sona are drawings made in the sand while telling a story or riddle. It’s one of the ways in which Chokwe elders impart knowledge and fables, though from what I’m reading the Sona tradition is dying out. They bear a resemblance to the Kolam of the Tamil-Nadu community in India, and even to traditional Celtic knots.

Math from other cultures is becoming really intriguing to me, and it’s an area I don’t think is covered enough in public education. Colonial era westerners often made the assumption that these “primitive” peoples didn’t understand some of the higher concepts of technology and mathematics, but if my studies have taught me anything it’s that we westerners were a little behind the curve (so to speak). At the very least, learning about how other cultures look at math and art can help us to see connections between ideas from new perspectives.

But one of the things I am wondering about is how to tell these stories respectfully. Some fables and tales are very private, specific to a culture, and not something that is intended to be shared with outsiders. Now obviously, since I don’t have the resources to travel to Angola myself, I’m getting these stories from people who’ve already spread them around. The genie is out of the bottle, so to speak. But it’s still important to consider their meaning, rather than to just include them as a pretty picture.

A lot of Adult Coloring Books have mandalas, in fact mandalas seem to be the stand-in term for most circular patterns in coloring books. I don’t think there’s anything wrong with enjoying these patterns, or designing new ones, and coloring them as a loose form of meditation. But at the same time I think it is also important to be respectful and understanding of the tradition. We want to learn and educate ourselves about a type of drawing, not just appropriate it.

Sometimes meanings for things change. The Kolam tradition seems to have had religious significance in the past, but now it is more a form of artistic expression by women in the Tamil community. Celtic knot constructions have a triune grid which reflects the triune nature of God, but also look really good on leather bound notebooks.

I’m a guy who wants to spread art and cool designs for their own sake, while also trying to explore some of the deeper meaning these traditions have to the cultures that created them. And I want to do that in a way that honors those traditions, without sharing them merely because they are exotic or different. The best way, at least for me, is showing the connections between some of the more abstract concepts of fractals, and their origins before they really came into their own (the days of computers and Mandelbrot). I’ve been thinking about fractals as something that is a new concept in math, but their origins may be much older.

I’m still working this stuff out, but I hope my intentions if nothing else can shape the writing in a good direction.