Check out Greg Egan's new page on caustics! The blue curve here is an ellipse. When we shine light on it, the reflected rays bunch up along a curve called a catacaustic. The ellipse is described by a quadratic equation, but its catacaustic is described by a polynomial equation of degree 6. This is an example of a general pattern discussed by Egan: the catacaustic of a curve of degree d has degree at most 3d(d-1). The math is serious, but the pictures will delight you!
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- Is the burnt out hard drive hyperbole or not? If it literally happened then I am curious if the code can be optimized to save the hard drive (or maybe it would be better to run it on some server somewhere)Jan 5, 2013
- Mathematica can be pretty memory-intensive. I remember doing my doctoral thesis work with it on a poor old Power Mac 6100 and making the hard drive thrash and thrash.Jan 5, 2013
- - Egan doesn't tend toward hyperbole. I doubt the hard drive literally caught on fire, but I think it really did stop working while he was doing a week-long calculation.
Apparently there's a virus that can make your printer catch on fire:
http://www.infobarrel.com/New_Virus_Sets_Printers_on_Fire_Is_Your_Computer_SecureJan 5, 2013
- - I woke up at night and remembered I wanted to add that explanation, but you beat me to it. The mathematical construction of a catacaustic as the solutions of a polynomial equation automatically throws in those 'virtual' points.Jan 5, 2013
- Sheila Miguez - Maybe implementing breaks allowing the drive to cool down would do the job.
Alternatively Egan should invest in a special AV (or server) harddisk if he wants to try this again. They're specially designed for working 24/7. I learnt about them in the VDR Portal. I'm running such a Linux-based DIY video recorder - with normal harddisks. My VDR is running 24/7, but obviously not recording all the time.Jan 5, 2013
- Jan 5, 2013