odd number

Drawing on protocol is a drawing constructed indirectly by its viewers, from the following rules:

1. The IP address of each visitor to this page is recorded in the site logs
2. The latitude and longitude of each visitor shall be estimated using a public IP look up service
3. The route from one visitor to the next in sequence shall be found using a public mapping service
4. If the route cannot be calculated from visitor i to visitor i+1, the route shall be attempted to visitor i+2, i+3, … i+n until one can be found
5. When a route has been found, it will be drawn freehand on the paper, the page representing a coordinate space of 360?Ǭ?x180?Ǭ?, with 0,0 at the centre
6. The hits will be recorded from the date of the first upload of this page, 20th June 2009
7. Repeat hits from the same IP address will be ignored
8. The drawing will be judged complete on whim, and no more lines shall be added

UPDATE 25th August: more lines added, and deemed complete. Most new entries were repeatedly in the same places – Seattle, California, or different network hubs in the UK and Europe.

UPDATE 2: best to do this sort of thing automatically, rather than with pencil and paper.

Timeline of mathematicians and the history of Paris

A simulation of the Poisson process, built using Processing.

The process models random events occuring in continuous time given that:

1. Events occur on their own
2. The average rate of events happening remains constant
3. Future events have nothing to do with ones which have happened

A process has average rate such as per minute. Number of events in t minutes is the discrete random variable X, where . The time you have to wait between events follows an exponential distribution .

The simulation works by obtaining a waiting time between each event, through making independent observations on the random variable . We can do this by solving:

where u is a random observation on the uniform distribution U(0,1). With the exponention distribution this means solving

which ends up with

Each time an event is fired, t is recalculated.

Western brands converted to Arabic in Abu Dhabi

Here’s the binomial distribution 80′s style. Each click generates a series of n independent Bernoulli trials resulting in a random variable Y which is the number of successes. The probability function of Y is:

where

This painting is derived from a finite projective plane of order 3.

Number of points and lines . Each line is incident with n+1=4 points, each point is incident with four lines. The projective plane corresponds to this cyclic block design which has thirteen varieties arranged in thirteen blocks of size 4.

There are small, persistent landslides from these cliffs every few minutes. Sometimes they can’t be seen, but you can hear the hissing noise. This is the result.

The beach has many blocks of stone containing fossillised shells. Lots of these stones have live barnacles and limpets firmly attached. It’s hard to tell what they think of their ancestors, but not that much seems to have changed over time.

I did two pictures today, but the other one looked a bit funny. It had pencil scribbles unfortunately near where you’d expect wibbly stuff.

Here’s the unfunny, serious, watercoloury one. I think the blue added at the end sorted things out a bit.