All Shapes in One Equation?

asadodetira writes ""One simple equation can generate a vast diversity of natural shapes, a Belgian biologist has discovered. Nature has the story. "The Superformula" sounds impressive, apparently its only for shapes, i thought you could solve lots of PDE's or tensor integrals or something with this, but not, it's only for shapes."

Comments

sounds familiar

[ddd2k]

Changing one term in the formula varies the proportions of the shape - moving from a round circle to a long and skinny ellipse.
This reminds me of the eccentricity ratio, C, of a conic function. It relates the parabola, hyperbola, and elipse. (eg, the parabola is the perfect shape as it has a eccentricity of 1 and the hyperbola >1 while the elipse is 1) However, im curious to what he did to transform a circle into various other shapes, which he did not mention in the article. big secret? ;-)

One equation...

[icemax]

One equation to rule them all, one equation to find them one equation to bring them all and in the darkness bind them...

now THAT's a nice ring-shape

Java applet visualisation

[FrenZon]

I have a java applet online that allows you to fiddle with the values in the equation and generate the 'super'shapes in realtime:

bodytag.org/supershapes1/

stop the presses

[g4dget]

Belgian biologist discoveres mathematics

After avoiding the subject for decades, a Belgian biologist discovers mathematics. One of the first areas he plays around with is "polar coordinates". "I never knew math could be this much fun", the biologist is quoted as saying. In his enthusiasm, the befuddled biologist decided to patent several formulas, following a recently fashionable trend of patenting the obvious.