Eric Weeks - personal pages - misc

Pictures of various mathematical spirals

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Click here to go back to my spiral triangles page.

See also the excellent page by Jan Wassenaar, which has even more examples than I show here.


Archimedean Spiral

radius = a * theta

Made with gawk script:

seq 0 0.002 1 | gawk '{t=5*$1*2*3.14159;r=t;x=r*cos(t);y=r*sin(t);print x ,y}' | psdraw -S 10 10 -X -30 32 -30 32 -l 0.1 >


Logrithmic Spiral (also known as an exponential spiral)

radius = a * exp(b * theta)

(I used a=1.0, b=0.1 for the above picture)

Made with gawk script:

seq 0 0.002 1.5 | gawk ' {a=1.0;b=0.1;t=5*$1*2*3.14159;r=a*exp(b*t);x=r*cos(t);y=r*sin(t);print x,y} ' | psdraw -X -111 96 -111 96 -S 10 10 -l 0.1 >

The spacing between loops increases exponentially.


Fermat's Spiral

radius = sqrt(theta)


Hyperbolic Spiral

radius = 1/theta


Lituus Spiral

radius = 1/sqrt(theta)

A "lituus" is a bishop's crook, I think.


Probably not an Exponential Spiral (?)

radius = ln(theta)

I just made this one up, I don't know if it's really called an exponential spiral or not. (I thought it'd be a good name, in analogy with the logrithmic spiral, but then Robin Garreck pointed out to me that the logrithmic spiral is also often called an exponential spiral.) The little tail occurs when log(theta)<0, that is, when 0 < theta < 1. It resembles a spiral named the "atom-spiral" (thanks to Annie Van Maldeghem for emailing me to point out the resemblance).


I found all of this information on spirals at Eric W. Weisstein's Treasure Trove of Mathematics.

Click here to get a copy of seq, a simple shell script which spits out a sequence of numbers (like a 'for loop'). Click here to learn about psdraw, a program which produces postscript output to make the graphs on this page.


Simple trigonometric plot | Double-trigonometric contour plot | Lissajous figures | Simple diffusion limited aggregation | Spiral triangles | Polar flowers

This page created June 12, 1997.

Current address:
Eric R. Weeks
Department of Physics
Emory University
Atlanta, GA 30322-2430