Matthew Conroy's blog

figure drawings

Sun, 2017-02-12 21:49

Some recent figure drawings.

Recursive 17-5

Wed, 2017-01-18 22:57

Messing around with recursion. Click for bigger on flickr.

recurse 17 - 5

animated eigenvalues

Tue, 2016-11-29 22:52

A little animation of eigenvalues of a 50x50 matrix with real entries which are a periodic function of time.

Larger dots for eigenvalues with larger magnitudes.

mozaic with extreme colors

Sun, 2016-09-25 22:33

Seeing a Chuck Close exhibit reminded me I wanted to try this again.
Choosing colors as extreme as possible to create a mozaic of a given image.

mozaic: extreme colors

pigeon wing

Sun, 2016-09-25 22:31

pigeon wing


Wed, 2016-08-31 20:41

Reflected in bent chrome.

ticket risk in Ticket to Ride

Wed, 2016-08-31 19:47

I've been playing a lot of Ticket to Ride recently. Jenni and I play with the 1910 cards. There are 69 cards total (so maybe this is the "Mega" game?). Each card has a point value. A player may choose to draw three cards: what is the expected minimum value of the cards drawn? This value can be interpreted as an upper bound on the "risk" associated with drawing tickets (cards): the worst case scenario when drawing is that you lose this minimum value worth of points.

The values on the cards are distributed like this:
That is, there is 1 card worth 2 points, 0 cards worth 3 points, 3 cards worth 4 points, etc., up to a maximum of 21 points (on two cards).
A little PARI/GP code:

Yields the array C:
[0, 2278, 0, 6436, 5860, 8560, 9660, 7259, 3202, 3683, 2856, 1060, 860, 225, 91, 144, 136, 0, 74, 10, 0]

Out of the "69 choose 3" possible hands, 2278 have a minimum card value of 2, 6436 have a minimum value of 4, etc.

From this we can calculate the expected value:
sum(i=1,21,i*C[i]*1.)/binomial(69,3) = 7.0304424170706...

What about the median?
Here's the array of partial sums of C:
[0, 2278, 2278, 8714, 14574, 23134, 32794, 40053, 43255, 46938, 49794, 50854, 51714, 51939, 52030, 52174, 52310, 52310, 52384, 52394, 52394]

So about 44% of the time the minimum will be 6 or less, and 62.6% of the time it will be 7 or less.
In fact, 89.6% of the time, the minimum will be 10 or less.

That's nice to know.

By the way, the average ticket value is 10.927... .

recent figure drawings

Sun, 2016-08-07 18:12

Been drawing on Fridays at Gage.

figure drawing

figure drawing

figure drawing

distance function video 36

Tue, 2016-06-21 15:44

Another in my series of distance function videos.

distance function video 36 from Matthew Conroy on Vimeo.

some recent things

Sat, 2016-06-04 16:14

exploded image: cat head

exploded image: spider

figure drawing: pencil

figure drawing: pencil