A monochrome pattern that’s simpler than it looks

The following pattern is, I think, quite pretty. I hope you agree.


Here’s how it was made.

  1. First I made a simple pattern in Windows Paintbrush.
  2. Then I made a copy of the pattern in step one, and flipped it. (Horizontally or vertically: it makes no difference.)
  3. Finally I merged the two to create the pattern you see above. A pixel is white if the corresponding pixels in (1) and (2) are the same colour (be it white or black) and black if the corresponding pixels in (1) and (2) are opposite colours.

Perhaps this will inspire you to create patterns of your own.

Links: 2015 — 8 (with a request or two)

I have, regrettably, been too busy to blog lately. But I’m here now.

There are two personal items I’d like to discuss, so I’ll begin with the first, follow it with selected links from around the Web, and finish with the second item. Both involve some kind of appeal for assistance, although one more so than the other.

The first concerns a card game I invented, and that we playtested at my birthday party last month.

[Update: This first request has been answered. I have shortened the text below to reflect this.]

My birthday was June 12, but for reasons pertaining to Dad’s recent retirement, it was one week later that a small celebratory gathering took place. There were five people present: a friend, an uncle, my parents, and myself (unfortunately, the uncle had to leave early). I left most of the organising and decision-making to my parents, but playtesting a card game was my one explicit request.

The game was one that I invented and blogged about in 2011, but at the time it was a work in progress and the rules yet to be fully refined. But recently I took it off the backburner, made a few small adjustments, and updated my original blog post accordingly.

The twist is that this is not a game you can play with the familiar deck of hearts, diamonds, spades and clubs. Rather it is designed for Ganjifa — traditional playing cards from India that are typically circular rather than rectangular with at least 96 cards per deck. Regrettably they are used for only a handful of games and even those are dying out. I don’t care too much about the traditional games, but it’s a pity that the cards themselves lack a living tradition of new games being invented. The world could do with more Ganjifa games, and the game I’ve invented is my contribution to that end.

Here’s where my appeal to the Internet comes in — because the one thing I have not managed to do is decide on a name for the game. Since it is played with Indian cards, I feel that giving it an Indian name would be an appropriate tribute to the culture that created them, and have been appealing for help from people who know Indian languages and are interested in helping to name a new card game.

If you can help, or know someone who probably can, I would greatly appreciate it. I’ve suggested the name केंद्र कड़ी (crudely: Kendra Kari) for reasons outlined in my Google Plus post, but I really require informed human feedback and not just the results of automated translation tools.

[Update: I’ve now received a response to this query and have updated the game.]

Now that you’ve read this far, here are some links:

Now to the second personal item.

A while ago, just for fun, I decided to see if I could guess an approximate formula for time dilation in general relativity. I didn’t expect to be right, but using a combination of high school physics, Ockham’s Razor, and a few elementary facts, I gave it my best shot.

So I was genuinely delighted to discover later that my result checks out against real-world examples!

This page on Quora has a couple of obvious faults (the biggie is that the altitude of the ISS varies between 330 and 435 kilometres according to Wikipedia, so calculating a result to so many significant figures makes no sense), but the relevant formula corresponds closely to mine. Moreover, plugging their result into my formula puts the ISS in the right range — at about 375 kilometres. Another example I found is that time goes faster by 10 nanoseconds per year for every floor you go up in a building; again, my formula checks out, putting the difference between floors at a very reasonable three metres.

I am no genius (trust me on this), but in all the popular science I’ve read, I have never seen anyone mention that an approximate but workable formula for time dilation in general relativity is astonishingly easy to guess. Feeling that I’d stumbled on an angle that popular writers have missed but would be useful to others, I decided to write up my results as an article of my own. Please remember this is an un-factchecked draft, and I am no more an expert than the target reader, but you learn by doing. It’s written in the style of a popular science article, and is 1000 words long.

If any real popular physics writer reads this — I would love to hear your feedback. Also, you are welcome to take inspiration for your own blog posts, and I hope you will be so kind as to send me a link if you do. A tweet to @GoldHoarder will do nicely.

(Incidentally, I used a free PDF converter, so the links don’t work, but since they’re fully spelt out they won’t slow you down very much. Since it’s a draft, I find this acceptable.)

[Update: I linked to my relativity article in a comment here.]

Links: 2015 — 4

There are several notable things to report on this month, though unusually, that doesn’t translate to a lot of links to share.

You’ve probably heard the news that Terry Pratchett died recently. I’ve been a fan my whole adult life, and this feels like the end of an era. There’s an official announcement here, plus various news reports, opinion pieces and tributes all over the Internet. Many are well worth your time, but I’m more inclined to encourage readers to look around than link to anything specific. There’s one last book to be published posthumously (confession: I’ve never read any of the Tiffany Aching books).

My sister’s second child, Elliot Roger Smith, was born around 11:15 on Wednesday March 11. I have yet to meet my new nephew, but I hear all is well, even if his big sister has some adjusting to do.

I now have over a thousand WordPress users subscribing to this blog. This means little, because the overwhelming majority are follow spam — people who follow other blogs indiscriminantly either in the hope that it will get them some attention or because they’re the blogging equivalent of hoarders — but there must be some who subscribed because they genuinely looked at my blog and liked what they saw. If that’s you, I encourage you to make yourself known in the comments. Tell me who you are and what you found here that you liked.

The Gede Ruins in Kenya are famous not only as a historical site but also for its wildlife (especially the monkeys), and a community organisation that helps to protect the site is now using a logo that I designed (though someone else drew the animal outlines). For a few months they were rather cheekily using a draft version that I only sent — along with some other designs — to show how things were progressing, but I don’t know the whole story behind that decision, and the completed version is in use now.

Now here are some links. Not many this month (for whatever reason I’ve not seen a lot recently that compels me to archive it) but I hope you enjoy them.

Vampire Women, a short story

I avoid sexual topics on this blog, for reasons best encapsulated in the phrase “more trouble than it’s worth“. I’d love to live in a world where a conversation about the diversity of human experience need not be approached with trepidation, but sadly, in the real world it does tend to bring out the irrational in people.

Today I’d like to lift the veil ever so slightly and share a short story I wrote in 2009. It includes the only sex scene I’ve ever written, and I’m actually quite proud of it. If you know me at all, you’ll expect a twist.

I published the story on Ficly.com, which I’ve written about before. Ficly was a site where people wrote stories in 1000 characters or less, but it has recently closed its doors — the archive is still there but you can no longer publish anything new. A new site, Ficlatté, has succeeded it, but it’s not much to look at so far.

Read the rest of this entry »

Fractal poetry, and other links

This post contains what purports to be a fractal poem. It’s not a bad poem in its own right, but the link to fractal geometry was too subjective for my taste. However, it got me thinking about what else a “fractal poem” might mean, and I was up till two that morning bringing my idea into fruition. I shared the poem I came up with in the comments, but a fuller explanation appears below.

I based my poem on a simple L-system. An L-system contains a set of rules, applied iteratively, for replacing one symbol with a sequence of symbols. For example, suppose we agree to replace “A” with “ABBA” and “B”, with “BA”. Then, starting with “A”, the first iteration gives “ABBA”, the second iteration gives “ABBABABAABBA”, the third “ABBABABAABBABAABBABAABBAABBABABAABBA” and so on. The connection to fractal geometry is that if we interpret the symbols graphically (e.g. “A” for “go forward” and “B” for “turn left”), we get a squiggly line whose squiggliness depends upon the number of iterations.

I used an L-system where “A” becomes “ABBA”, “B” becomes “BCCB”, and so on. (Using numbers rather than letters, this is: “n → n, n+1, n+1, n”.) After two iterations, we have “ABBABCCBBCCBABBA”, which is the structure I used for my poem, interpreting each letter as representing a line and requiring all lines assigned the same letter to rhyme. In other words, it had to be a 16-line poem in which lines 1, 4, 13 & 16 rhyme, lines 2, 3, 5, 8, 9, 12, 14 & 15 rhyme, and lines 6, 7, 10 & 11 rhyme.

Here is the result. It has, I think, an interesting aesthetic quality when read aloud.

This doggerel does not intend
To satisfy the reader’s would
For art that is remotely good;
It will not serve to meet that end,
So don’t imagine that it could.
But in its rhyming structure you
Might find, if you are able to,
A pattern to be understood
That’s relevant to trees of wood
And clouds of water vapour, too –
The applications are not few –
For it possesses fractalhood.
Look closely, and you’ll comprehend
The secret pattern, bad or good,
Which, if this text were longer, could
By iterative means extend.

After a third iteration, the structure would be a challenging ABBA BCCB BCCB ABBA BCCB CDDC CDDC BCCB BCCB CDDC CDDC BCCB ABBA BCCB BCCB ABBA. Four iterations would give you an epic poem of 256 lines. You’re welcome to give that a go, or maybe you’d prefer to write your own variation on a shorter poem like mine.

Here are some more links that I found over the Christmas holidays:

  • The development of a foetus, animated.
  • Strong Language is a new linguistics blog about swearing. Mostly. Along the way it covers a variety of topics and is worth a look.
  • A well-presented and informative video on placenames ending in -stan.
  • A curious difference between the Andromeda Galaxy and our own.
  • All of the best arguments against vaccination together on one page. (No, it’s not blank, but you’ve got the right idea.)

As for the holidays themselves, I don’t feel like writing a report, but rest assured I had an excellent time. Here are two photographs that capture some special moments.


The photo on the left shows my niece and her parents (my sister on the left, pregnant with her second child) at the Christmas table as it is being prepared. Of note are the origami mangers, complete with jelly baby and paper straw, alternating with paper trees. The brown paper bags are what we used instead of crackers.

On the right is a framed photo set showing miscellaneous moments in Elke’s life so far. This was Rebecca’s Christmas present to me, and it is now hanging above the light switch in my bedroom.

Winning Cosmos

This is the story of a competition I recently won.

In an episode of the Skeptic Zone podcast published while I was in Sydney, Richard Saunders announced a competition: to take a photograph on the theme Billions and Billions for a chance of winning a DVD set of the recent Cosmos remake.

Being on holiday I wasn’t planning to enter, but I did spend some time thinking about what sort of photograph one might take (it also made a good conversation topic). I decided that hundreds and thousands should feature somehow, and my best idea — given the time, resources and skills to pull it off — was as follows. (1) Bake a cake in a small, hemisphere-shaped bowl, and ice it to look like (half of) a giant hundred-and-thousand. (2) Choose a background for the photograph that represents the void of space  — perhaps a dark cloth laid over some surface — and sprinkle hundreds and thousands all over it. (3) Place the cake amidst the hundreds and thousands; and on top of the cake, place a lego figure with a telescope.

I don’t have the resources to create this, but obviously there are people out there who could pull it off, and probably do something even better that I hadn’t thought of. So I didn’t think I had any hope of winning the competition, and was just hypothetically contemplating what I would do.

Then I went along to the August 7th Skeptics in the Pub (as described in my Sydney report), and chatted to some people from the Skeptic Zone podcast. The photograph competition came up in conversation with Jo Alabaster, who strongly encouraged me to enter, saying that there had been very few entries, and that even a diagram of my idea would be worth sending in.

My original idea might have been at the edge of possibility given enough time and borrowing of resources, but with a deadline just two weeks after the original announcement (more like one week by the time I got home from Sydney), it was completely impossible. Still, by now I knew that a simpler photograph was in with a chance, and the Cosmos DVD set was a pretty alluring prize. Then — as I was contemplating what resources I might find on an upcoming grocery shop — I hit on an idea that was easily within my grasp, and a multi-layered interpretation of the challenge. All I needed to buy was one bag of icing sugar.

At some point I looked up the other entries on the Skeptic Zone facebook page, and indeed there weren’t many. This surprises me: the much-talked-about Cosmos series is surely an attractive prize, and not something many Australians would have seen already (people who subscribe to non-free-to-air TV are a small minority); I saw one episode on Youtube before it was taken down.

You can find my entry here, and I’ve also replicated it below. Here is the photograph:


And here is the explanation I sent with it. (A note on the calculation: if you google the size of an icing sugar particle, you’ll find figures between 10 and 100 micrometres. I used 100 cubic micrometres for my estimate … wait, that’s wrong, isn’t it? A cube 10 to 100 micrometres across is actually 1,000 to 1,000,000 cubic micrometres … call it 100,000 cubic micrometres … and a billion particles that size would take up a tenth of a litre … whoops, now I’m embarrassed.)

It’s a pair of equations, one horizontal, the other vertical, like a crossword. Physical objects stand in for quantities

The first equation reads: “100s & 1000s cubed is less than icing sugar”.

If hundreds and thousands (the famous confectionary) are called hundreds and thousands, then icing sugar could very reasonably be called billions and billions. In fact, I calculate that just one millilitre of icing sugar contains more than ten billion grains!

The second equation reads: “earth multiplied by icing sugar is less than universe”.

This ties the photograph to a cosmological theme, asserting that the universe contains the equivalent of billions and billions of earths.

By the time the deadline arrived I was expecting to win (although I liked the elegance of Jon Frary’s entry), and throughout the next day, tension was high. I checked the relevant links over and over, and as time passed I thought maybe I hadn’t won after all.

Then — about 31 minutes into episode 304 of the Skeptic Zone — the official announcement … I won!

I look forward to the DVDs. I’ve read enough reviews to know that the series is flawed — just like everything else in the real world — so I am not expecting perfection. I do, however, expect it to be very good, and that its strengths will outweigh its flaws by a considerable margin. Perhaps I will tell you what I thought.

Incidentally, long time readers will know this isn’t the first time I’ve won a science-related online competition. Last time I wrote a limerick.

Manual variation on the snowflake curve

Ever since I created the following image more than a year ago, it has inhabited that uncomfortable limbo of being too good to delete and too trivial to share. But then, a blog needs the occasional triviality, so here it is.

It’s a version of the famous Koch snowflake curve, but with a different-from-usual presentation. I can’t remember the precise method I used to draw it, but it was done manually in a version of Windows Paintbrush, and not with the help of any more specialist tools.


A cruel-coloured scathed crow

Audio pareidolia applied to song lyrics is a potent source of comedy. A single misheard line is often amusing enough, but the illusion is taken to another level when the imposed and original lyrics are in different languages. You may remember the Four Tuna video that went viral several years ago, in which a very well-known Latin song is given English captions that somewhat resemble the Latin phonetics. The result is simultaneously hilarious and fascinating.

I have listened countless times to the Youtube video of Karan Casey singing A Chomaraigh Aoibhinn O — an extraordinarily beautiful Irish song. I first linked to it in 2008, and it’s still a favourite. The lyrics, alongside an accurate English translation, are available here.

Recently I decided to give it the Four Tuna treatment, and my fake English lyrics are given below, underneath the original video. You can follow along and see how well my false lyrics fool your brain.


Moving hard down creek,
Nor the kid is still related;
I come back heaving gold.
Store the vine, though a cool work,
And your do will clearly fail all;
I come back heaving gold.
Laugh, ha-ha, yellow well,
Spoke a kind-hearted greybuck;
The gloam does swallow
The font of the layerer.
Oh, Grandma Creek,
It’s suet lower K, lol,
I come back heaving gold.

If stone grew barren
At a cruel-coloured scathed crow,
I come back heaving gold.
Through the last seven sewers,
Little heart’ll want a grainer;
I come back heaving gold.
Our fastest larrikin,
Here gone the pathed fields;
My wrath I show,
Let it show o’er the glazed fair.
Wrote a scar, penned and drew it,
And a new sort of spare art;
I come back heaving gold.

Nor veer sour or solar,
Shadowly we came, which
I come back heaving gold.
He knew we’d get fond
And yearn, let it stay here;
I come back heaving gold.
Our barber carried on,
Got a new sort of cradle;
If a heart got barred,
Fish can like a late shift.
It’s cost me a legion,
I flew a lot of leisure;
I come back heaving gold.

I vaguely entertain the notion that a skilled satirist could weave some story around these words — as another layer of pareidolia, that would be somewhat fitting. They’re utterly meaningless, of course, but it does no harm to caution readers in Ireland to watch out for the cruel-coloured scathed crow, just in case.

Does it work for you?

[I originally shared this on Google Plus — which is sometimes useful for sharing things that are still taking shape in my mind, with minimal attention to presentation or how they might seem in retrospect — but I’ve decided it merits a place on the blog.]

Fragments of song

There are several old posts on this blog about music that I composed when I was younger. But as a teenager in the nineties I also composed some fragments that never became complete songs, and I’ve not yet blogged about those.

So here is a selection. The lyrics are brimming with teenage angst, and are also rich in words I thought of as inherently poetic at the time. If any of them inspire you, you’re welcome to adapt them in your own creative works. All I ask is that you let me know.

Most of the recordings below were made expressly for this blog post, and are not polished performances. Their purpose is simply to demonstrate the tune.

The first one is the chronologically oldest, and here is a tune I recorded some years ago, followed by lyrics:

What I feel is a kind of torture
Every moment reminds me of a thought that once occured
And I feel nothing less than torture
When I remember that the thought is too absurd.
I cannot justify the course this tension’s leading;
I wait unsatisfied, in pain and almost screaming.
Waiting for some release from torture
To release my mind, a thought that’s not absurd
And I feel nothing less than torture
When I remember that the thought has not occured.

The next fragment is intended to sound like some old folk song. It’s rich in metaphor and open to interpretation.

There is no place so distant as my only world;
There is no sound so faint as our most piercing scream.
What shall I build, here where a thousand stones are hurled,
And where the wind erodes away each worthless dream?

This one is about being abandoned by a valued friend. The second verse would have included the line, “And I’ll walk to infinity again today” (invoking a sense of aimlessness).

Every healing word I know is void;
Watching silence greet every desperate cry.
Everything we shared, everything we said;
Watching memories freeze as they pass me by.

A few years ago I wrote the above fragment into a story — as previously mentioned here — and also included this one.

How do I build from impossible stones —
Where’s the ground to hold them?
How do I walk from infinity home
After wandering there?

To finish, a fragment that is only one line long, but which I’ve always thought has potential for a pop song.

Unwelcome conclusion of a painful illusion.

I hope these brought you pleasure, and that they don’t evoke your current state of mind. But you have my sympathy if they do.

The Gzarondan language

Among the blog posts I’ve revised in my current archive clean-up is my 2006 article on conlanging. That blog post discusses artistic language invention in a general way, but makes only a passing mention of my own conlang, Gzarondan.

That’s because I didn’t have any documentation ready to share. Last time I’d worked on the language, I’d left a lot of details in flux, so the documentation I had was a bit of a mess. But although I have no plans to do any more conlanging in the future, I did always want to publish an official documentation of the language I created. Sometimes it just takes a few years of cold storage.

To that end, I published a short article about it near the end of 2012. This document has been sitting quietly in case further editing proved necessary, but I’m ready to share it now. First, though, a few words on what this documentation is and is not, because many conlangers are used to documentation written by other active conlangers, and this governs their expectations.

I spent a lot of time working on the Gzarondan language back in the day, but for most of the decisions I made (or periodically changed my mind on), I simply don’t care anymore, so I have no interest in documenting them. What I’ve written therefore documents only the aspects of the language that I feel some attachment to: The Best Of Gzarondan. Everything else has been discarded.

To make this possible, I’ve taken the perspective of an outsider, describing the language as if it were something I’d read about in an old scroll or something. That way, if I don’t wish to document some feature, I can simply describe it as “unknown”. Other conlangers are welcome to build on my creation, or to simply pinch some ideas here and there for their own art.

You can read my five-page article on the Gzarondan language here.

[Minor corrections made to PDF document on February 9]