Posted by Dave Mark on Nov 15, 2009 in
Math,
art Remember fractals? Fractals were discovered by Polish-born mathematician Benoît Mandelbrot. They are the set of numbers whose origins lie with the equation:
zn+1 = zn2 + c
where the set remains bounded as n increases.
Without worrying about the math (you can read about the math here), the beauty of fractals lies in the images they can produce. Here’s a typical example:
Fractals have fascinated mathematicians and digital artists since they first gained fame in the mid 1970’s. The mathematics of fractals are complex, but well defined, though one mystery has teased mathematicians since fractals were born. As you can see from the image above, fractals are a 2D kind of critter. Part of their charm is that you can zoom in infinitely to an everchanging image (here’s a fantastic example), but that image remains flat. The pursuit of a 3D Mandelbrot set has been a fractal holy grail for more than 30 years. Over the past few years, real progress has been made, culminating with work like this:
If you are interested in seeing more of these haunting and complex images, take a click over to this page. Lovely stuff…
– Dave
Tags: 3D, Fractals, Mandelbrot, Mathematics
Posted by Dave Mark on Nov 2, 2009 in
Math From my cousin Allen. Absolutely love this. Go into Google and type in this expression:
5*9+(sqrt 9)^3
Here’s the result I get:
Exactement! Just so! Now type in this expression:
599,999,999,999,999 – 599,999,999,999,998
And here’s the result I get. Wow!!!
Want to know why this sort of thing happens? Read this terrific article by Mike Bedford. In a nutshell, computers represent numbers as powers of 2 or fractions built on powers of 2. Assuming a limited number of digits to represent numbers, there’s only so much accuracy you can achieve. The key for developers and spreadsheet users alike is to know the limitations you are dealing with. And build safeguards into systems on which life depends!
– Dave
Tags: calculator inaccuracy, Computers suck at math
Posted by Dave Mark on Oct 23, 2009 in
Math,
art Go to the page linked below, hover your mouse over the page and just wait. After a bit, move your mouse and wait some more. Hypnotic…
Here’s the link…
– Dave
Tags: art, Math
Posted by Dave Mark on Sep 17, 2009 in
Math From my buddy Todd, this one’s fun:
Head over to this site, pick a number, add the digits together, subtract the original number, then Psychic Math Friend will guess your number.
Know how this works? I’ll post a comment with the math…
– Dave
Posted by Dave Mark on Sep 16, 2009 in
Math Thanks to Joe Ekiert for this mind-twisting pic. Don’t get it? Leave a comment…
– Dave
Tags: Math, Pi
