Not really self-referential; still cool though

I was inspired when reading about Tupper's self-referential formula to derive my own version of such a formula. The formula looks impressive but isn't really too difficult to understand or derive from scratch. (And it isn't really self-referential either as it creates all possible bitmaps. The trick is just in figuring out how to find the right region of the graph that contains your bitmap.)

So I wanted to do a simple 10x10 bitmap containing an image of "Hi!". After a bit of work on paper I got to this inequality, where w and h are the width and height of the region respectively:

It's a bit better than Tupper's one because it plots things uninverted, i.e. the way you'd expect them to be

So, after creating a quick Python script to calculate k, the starting y-coordinate on the graph, which is a massive 6165710764903459078666956800 (for my formula only, not Tupper's original one), I got this plot:

Hooray!

Botswana home

It's about time that I add some photos of where I live when in Botswana. These were taken this morning.

The landy only just fits in

More context...

From the other side; the kapok tree is doing rather well

A long weekend (but only at 93.3% availability)

It's supposed to be a long weekend and it is for all of us but me, because Monday 27 April is not a holiday in Botswana. At least I'll be working from home.

Here are some weekend photos.

Neil has started spending some time sitting on the Dumbo

Sibling permutations

Pieter coming to terms with infinite recurssion

Coffee time this afternoon at Mugg and Bean

 We paused at the playground after walking back home after coffee.

Traversing the tube

Browning, in more ways than one

Browning 1: as mentioned previously, we've been suspecting that Neil is going to have brown eyes. That seems more and more certain every week.

Apparently passport photos have to show one's ears; Marisa says they had to take loads of shots of Neil before that requirement was fulfilled (just barely); the equations aren't relevant, they happened to be there and I left them in because I think they add flavour

Browning 2: autumn is gradually shifting to winter, and so too is the outdoor colour spectrum shifting towards the lower frequencies.

Snapped from my Botswana balcony this morning, the kapok tree is slow, having only just sprung into bloom

Browning 3: evening temperatures are low enough these days to allow us to make use of our fireplace, especially in connection with marshmallows.

The Maillard reaction in action a few nights ago

Roll and pitch done; awaiting yaw

One could think of Neil's mobility not just in terms of self-propulsion, which is still a long way off (I think), but also in terms of his ability to change orientation, which is starting to be more under his control. So I propose using the angles of rotation around x, y and z axes for this purpose. These are the roll, pitch and yaw angles respectively, and are defined relative to Neil as in the following pictures:

Neil as viewed by the most ordinary people

How engineers see him

Neil has already progressed well with pitch changes (lifting himself up with his arms when lying on his tummy), albeit through a fairly narrow angle. Still, it's not at all bad considering he's merely 13 weeks old.

An impressive pitch angle

Neil has now started with rolling, as he demonstrated to his doctor yesterday.

Start of roll

Half way done

Maybe this is the start of a yaw

Laughing Neil and a weight update

Marisa got to Neil laugh out loud for the first time on Saturday. It seems he's got a ticklish tummy. I caught the end of it:

Neil went back to his doctor for a check-up this morning, which means there's finally another data point for my graph! Hooray! The doctor says all is well. Marisa says Neil pulled out all the stops while there and performed his first roll (turning from lying on his tummy to lying on his back) to the doctor's delight.

We're just left with the logarithmic model now (it's the green line); the thick blue line is the actual data

Pieter's first rugby match

Pieter took part in two rugby matches this morning. The Midstream team played against Laerskool Wonderboom (at Laerskool Wonderboom). Miekie wasn't there as she went to a friend's birthday party. Here are some photos and videos.

Before the first match

Some spectators

 After the rugby Marisa, Pieter, Neil and I had some coffee (and hot chocolate) before heading back home.

A time-lapse

I've been taking regular photos, whenever I've been in Botswana, of the construction work taking place outside my office window. The building is very close to complete now so I thought I'd create this time-lapse. The photos span from November 2013 to April 2015.

Slightly quicker than it happened in real life

Back home

We made it back home safely yesterday. We left the house in Langebaan at about 8:00 in the morning, returned the keys to the estate agent's office, drove to Cape Town in heavy fog all the way, flew back and got a lift home from the airport. Neil handled it all extremely well, particularly the flying, which he spent sleeping. He's become a bit of a fussy car passenger though, preferring to complain (i.e. cry rather intently) if he happens to be awake, for no discernible reason at all. So there was a bit of that along the road from Langebaan.

Here are a few miscellaneous Langebaan photos that didn't form part of previous posts.

At Pearly's (using the back camera)

At Pearly's (using the front camera)

Car-spotting (and a little lesson in basic statistics) from on top of the garage while the other three went shopping

Pieter is rarely as impressed by food as he was by Friday Island's ribs (the shark seemed keen for some too)

Smiles and a start

A visit to Kersefontein

My parents, Ali's parents, Alexander and Misha, and Marisa, Miekie, Pieter, Neil and I popped out to Kersefontein for a quick visit today.

Everything is photogenic...

... even most of the animals

Panorama with the family graveyard on the hill to the left

Pieter next to the plaque commemorating his great-grandfather Pieter

More photogenic subject matter... and an old building

A cottage

Lawn-swine indulging in a nibble

Neil seemed to enjoy it all too

Pieter fizzled out a bit at one point...

... but Miekie was greatly inspired by Julian to become a farmer one day

Pietered out boy, lovely lady, random pig

Every visit to Kersefontein invariably includes some spontaneous photos on the front lawn

Julian's dog doesn't let anything get in the way, including gates...