Posts for Tag: art

The Mona Lisa As Drawn By A Traveling Salesman

Posted In: Fun | Math
Mona Lisa TSP
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The traveling salesman problem (TSP) is a classic problem in operations research and mathematical programming. It seeks to answer the question, given a set of destinations, what is the shortest possible travel route someone could take to visit them all. It is a notoriously challenging problem to solve when the number of destinations grows. A picture of the famous Mona Lisa was converted to 100,000 dots and a challenge was created to find the most optimal solution to visiting each of these 100 thousand points (i.e. drawing the shortest continuous line that goes through each and every point.
The current most-optimal solution that has been found to this Mona Lisa challenge was calculated in 2009 by Yuichi Nagata. This art is created using the order of destinations (also called the “tour) that he developed.

Click the “Draw Mona Lisa” button below to see the famous painting drawn with a single continuous line with 100,000 segments.

Each time you click on the “Draw Mona Lisa” button, it chooses a different starting point but follows the same order of destination points, looping around until all the points are visited.

You can also change the speed at which the individual line segments are drawn. It is surprisingly relaxing and satisfying to watch the line wind its way around the screen to fill in the famous picture of the Mona Lisa.

For a very high res version of the entire photo click here (around 4 MB file size).

Data and Tools:
I downloaded the 100,000 points and optimal tour from Yuichi Nagata from the TSP Art website and the University of Waterloo.
Javascript was used to draw on the HTML canvas and animate the process.

mona lisa tsp

Planetary Art – Inner Planet Orbital Spirograph

Posted In: Fun
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Earlier, I had made a visualization showing that Mercury is the closest planet to Earth (on average) and not Venus or Mars. To make that, I downloaded a bunch of NASA ephemeris (orbital) data. I realized I could use the same data to make some cool orbital art inspired by a spirograph – a planetary spirograph.

Basically, you get to choose a planet and the visualization will draw a line connecting that planet and Earth every few days. These lines will then build up into a cool pattern over 40 earth years of orbital cycles. Each planet (Mercury, Venus and Mars) has a different orbital period around the sun than Earth does and as a result, interesting patterns emerges.

Orbital periods of the four inner rocky planets:

  • Mercury: 88 days
  • Venus: 225 days
  • Earth:365 days
  • Mars: 687 days

Also evident is that the orbits of some of the planets are not quite circular so the pattern isn’t quite centered on the sun. Venus has the most regular pattern, creating a distinctive 5-lobed design. The other planets also have visually stunning patterns, though they do not repeat perfectly over time.

You can change the planets using the drop down menu as well as change the speed of the spirograph, and hide the planets and the sun.

Data and Tools:
I had thought about simulating the planets but there are plenty of tools out there that generate this orbital data so instead just downloaded 40 years of ephemeris data (data related to positions of astronomical bodies) from NASA website.. I processed the data using javascript and drew the picture using HTML canvas tools.

Planetary Art Spirograph