Yesterday, when I was having some Christmas lunch at a sushi restaurant with my 16-year-old son Aaron, the conversation turned to fractals.
I’m curious. Do you know what a fractal is?
If you look up “fractal” on Wikipedia, this is the first thing you’ll find:
This article may be too technical for most readers to understand.
I don’t know the meaning of that little cleaning brush,* up there on the left. Is Wikipedia warning us that the “Fractal” article needs to be cleaned up and de-technicalized, so most people can understand it? Or is Wikipedia suggesting that readers should brush up on their knowledge of fractals, starting now? Or is that brush actually an example of a fractal?
Here’s what inspired the discussion of fractals yesterday: Aaron was folding paper, like so, while we were waiting for our food.
While he was folding, Aaron asked me if I knew what a fractal was.
Do you ever think you know something, until somebody asks you to explain it? As I tried to access my memory of fractals, I was imagining interesting, intricate patterns involving branching and lines getting smaller and smaller. I wasn’t sure that was correct, though.
Aaron told me that a fractal
- contains itself and
- is repetitive.
I wondered, to Aaron, if I were a fractal, because I can contain myself and I am sometimes repetitive. (If you don’t believe me, just read more of my blog posts.)
According to Aaron, I am not a fractal. I’m not sure what Wikipedia would say about this, since I stopped reading that article once I saw the cleaning brush.
I wondered, at the sushi restaurant,** if these things were fractals:
I then said something, to Aaron, that I’ve repeated before. That is, I mused out loud that the topic under discussion might be a bloggy one. To my surprise, Aaron expressed an opinion that “Fractal” WOULD make a good title for a post. I’ve never heard Aaron repeat something like that before, and I could hardly contain myself. So I knew I HAD to write a post, today, titled “Fractal.”
That brings us up to now.
This post now contains a dilemma, that my other blog posts** repeat and contain. How can I write a blog post which
- has the chosen title,
- contains myself (truly and authentically),
- repeats, in a contained way, enough of my previous insights, for continuity, and
- contains and repeats a worthwhile experience for my readers?
This post contains something else that repeats for me: Once my mind contains an awareness of something, I see it repeating, wherever and whenever I am.
That is, once I was aware of fractals yesterday, I saw them everywhere. When I went for a Christmas Day walk, I looked for and saw fractals:
Are those really fractals? What is your fractal impression?
When we visited my boyfriend Michael’s family** later in the day, were there fractals there?
That last photo not only contains curves (which Aaron names as an important component of fractals), it also repeats bongos (seen previously here, here, here, and here).
I don’t think YouTube** contains any repeating song named “Fractal,” do you?
This was as close as I could get:
That’s “Fragile,” in a live performance** by Sting (who created that beautiful song) and Stevie Wonder (found here on YouTube).
Because I’m a psychotherapist AND a human being who has dealt with medical challenges my whole life, I contain more repeating knowledge and understanding about “Fragile” than I do about “Fractal.”
But that didn’t stop me from writing this today, did it?
Before I end this post — so I can, perhaps, go see fractals at cardiac rehab** and at work,** too — here’s another photo, which I just snapped:
Regular readers of my blog** might have expected that photo to contain and repeat one of my cats, Harley or Oscar:
I’d explain that photo, if I had time, but I’ve got to fractally and fragilely run. Any guesses why I included that photo here (and whether it contains fractals)? Any fractal-post-related questions?
Thanks to Aaron, to Michael, to Michael’s family,** to Wikipedia,** to Sting, to Stevie Wonder, to Genki Ya Sushi,** and to all who read these posts, no matter how fractal or fragile you are.
* Apparently, your experience of this post may or may not contain one picture of a cleaning brush.
** Which may contain those who may or may not understand fractals, like me.
I thought I knew what a fractal was too … but I didn’t … now I do.
Thank you Ann!
Enjoy the fractal festivities today 🙂
I did enjoy the Fractal Festivities today, Val. Thanks for joining in with me today. Now I’m off for another Friday Fractal Festival, tonight.
You crack me up – I had a student once who wrote thousands of words about fractals, read his thesis to me and my neck has never recovered from nodding wisely – argh!
I’m sure you nod wisely a lot, Julie. I’m glad I cracked you up!
My son, Matt, wrote his college application essay about fractals. That was 12 years ago. All I can remember of it were 2 words: fractals (of course) and iterations. When I saw your post today, I went looking in his room (where the detritus of his youth still remains, though he no longer lives there) to see if I could find it. I don’t think we have it as a word document anywhere…probably lost when his computer had a meltdown when he was in college. We didn’t think of backing anything up back then. So now I am sad (maybe wistful is a better word) that his brilliant essay may gone for good. Perhaps I will unearth it at some point as I proceed with the archeological dig in his room. That may take decades. I suppose there is the possibility that his essay is archived somewhere at his alma mater. Maybe they hang on to these things forever on the chance one of their alums might someday be famous and these papers will then become artifacts. I did find his SAT and AP scores (why did I save those???) which the Matt museum might want someday.
I love the Matt Museum — sounds like a great place to visit. Many thanks for making your way to the Ann Museum today.
will try to
piece this together
when feeling
less fragile 🙂
you may have
pieced it together already.
thanks for your strength and
fragility.
Now I know, Ann. Did I need to know? Will I need to know? Should I know? The answers all curve and intersect and are self-contained. Like a fractal. One woman’s fractal is another man’s tree branch of knowledge.
Which woman and man are we talking about, Mark?
Now that I’ve asked one question, I shall attempt to answer all of your fractally questions:
1. I’m not sure.
2. I can’t predict the future.
3. “Should” is often an unhelpful concept.
Thank you for helping me understand, again and iteratively.
I was too oblique and obtuse. Freaking fractal through me for a loop, Ann.
Or threw me for a loop, too.
No need to repeat, Mark. The “through” threw me not.
Your blog is full of fractals, Ann. It’s a kind of excursion of inner recursion: expanding and tessellating. You’re a master of literary and psychological fractals both fragile and powerful. Geometry across more than 3 dimensions.
You use words like “tessallating” and I’m the master? Thanks for this multi-dimensional appreciation.
But Aaron is very good with paper-folding. Like his mom, he has such an intriguing combination of strengths: artistic, mathematical, musical, logical, conceptual. I wonder if he will head towards engineering? Theatre? Medicine?
I think Aaron could do anything. ANYTHING. I look forward to watching him go wherever he does.
I had to look this up. I found a definition of fractal in the simple wikipedia. You were so right about the regular wikipedia, but the “simple” one makes some sense to me.
At the very least, I now have a new Scrabble word!
There’s a SIMPLE WIKIPEDIA? Now I have to go look that up. Thanks for continuing to teach me things, Emilie.
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I used to have a fractal screensaver and it was mesmerisingly beautiful and very distracting. Thank you for reminding me.
I’m always glad to remind you, Hilary, and I’m always happy to see you here!
I’ve read a lot about fractals but still don’t fully understand them – I only know they create beautiful visuals I could happily stare at for hours. My left brain doesn’t get them but my right brain loves them!
How wonderful, Annabelle, that you are open to both sides of your beautiful brain!
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