Eric Weeks - personal pages - misc

Polar Flowers

Another very simple idea I got from a book. See the bottom of the page for links to other simple algorithms like this one.

weeks@physics.emory.edu

This idea came from a book called "Mathographics" by Robert Dixon. Simon Pick gave me this book; thanks, Simon! Click here for a Java Applet that lets you play with these ideas interactively. Written by Adriaan Vannuffel. It's written in Dutch, but just try typing in numbers and see what happens.

This was created with the following gawk script:

gawk ' BEGIN { for (rad = 5;rad<45;rad++) { for (theta=0;theta<=2.0*3.14159265;theta+=0.01) { r = rad*(8 + sin(theta*6+rad/10)); x = r*cos(theta); y = r*sin(theta); print x,y; } } } ' | psdraw -c0.02 -f0 > rose1.ps

I think the gawk script is fairly self-explanatory. The "rad/10" gives the figure a slight phase shift as it grows larger, resulting in the spiralling effect. You need to use gawk, not awk, as awk does not have trigonometric functions. This could all be done very easily in BASIC or C or whatever.

Other pictures using this idea:

gawk ' BEGIN { for (theta=0;theta<=45*2*3.14159265;theta+=0.008) { rad = (0.8*theta/(2*3.14159265)+3); r = rad*(8 + sin(theta*6+rad/3)); x = r*cos(theta); y = r*sin(theta); # this next line sets the COORDINATES: print x,y; # this next line sets the COLOR: print 0.5+0.5*sin(theta*6+rad/12),0,0.5+0.5*cos(theta*6+rad/10) } } ' | psdraw -c 0.02 -CO > rose3.ps

gawk ' BEGIN { for (theta=0;theta<=45*2*3.14159265;theta+=0.008) { rad = (0.8*theta/(2*3.14159265)+1); r = rad*(8 + sin(theta*7+rad/1.8)); x = r*cos(theta); y = r*sin(theta); # this next line sets the COORDINATES: print x,y; # this next line sets the COLOR: print 0.5+0.5*sin(theta*7+rad/12),0,0.5+0.5*cos(theta*7+rad/10) } } ' | psdraw -c 0.02 -CO > rose4.ps

Click here to get a copy of the above shell script.

gawk ' BEGIN { for (rad = 10;rad<60;rad++) { for (theta=0;theta<=2.0*3.14159265;theta+=0.007) { r = 8+rad*(0 + sin(theta*6+rad*3.14159265/2)); x = r*cos(theta); y = r*sin(theta); print x,y; } } }' | psdraw -c 0.04 -f 0 > rose7.ps

gawk ' BEGIN { for (rad = 5;rad<60;rad++) { for (theta=0;theta<=2.0*3.14159265;theta+=0.007) { r = rad*(8 + sin(theta*6+rad*3.14159265*.9)); x = r*cos(theta); y = r*sin(theta); print x,y; print 0.5+0.5*cos(theta*6+rad/12),0,0.5+0.5*cos(theta*6+rad/10) } } }' | psdraw -c 0.02 -CO > rose8.ps

gawk ' BEGIN { for (rad = 5;rad<60;rad+=4) { for (theta=0;theta<=2.0*3.14159265;theta+=0.007) { r = rad*8 + (16*sin(theta*6+rad*3.14159265/4)); x = r*cos(theta); y = r*sin(theta); print x,y; } } }' | psdraw -c 0.08 -f 0 > rose9.ps

Click here for more information on psdraw.

Click here to learn how to convert PostScript to GIF.

Links...

Odds and Ends: These are various tiny ideas that are simple to do which make interesting pictures, or are otherwise interesting (to me). Click one of the pictures below to see others.

Eric's Home Page
Other software
Pictures I've made -- fractals, quasi crystals, cellular automata
My research -- what I get paid for
Graphics Techniques
Questions? Comments? Send me email; email address below.

This page created September 4, 1996.

Current address:
Eric R. Weeks
weeks@physics.emory.edu
Department of Physics
Emory University
Atlanta, GA 30322-2430