Back to . . .  NCB Deposit #73 ONONDAGA Community College SUNY A Collection of Famous Plane Curves created in POVRAY (Persistence Of Vision RAY tracing) Patrick J. Gleason pgleason@twcny.rr.com
The Joy of Mathematics
Color-coded Curves

In each of the pictures below, x is the horizontal dimension (width), y is the vertical dimension (height), and z is the color (depth). To more clearly show the contours of the z surface, the color has been quantized (summarized) into 16 distinct levels:

 0 = BLACK 1 = BROWN 2 = RED-BROWN 3 = RED 4 = ORANGE 5 = YELLOW-ORANGE 6 = YELLOW 7 = YELLOW-GREEN 8 = GREEN 9 = CYAN 10 = BLUE 11 = INDIGO 12 = VIOLET 13 = BLUE-GREY 14 = GREY 15 = WHITE

The drawing program plots thin black lines to represent the x and y axes, and a thin white line to show where the 3-dimensional surface crosses the z=0 plane. You can click on any picture on this page to see a full-screen version that you can study in detail.

 Circle r = cos(q) z = x/r - r Drawing Limits: (-2, -2) - (2, 2) Min z: -3.3, Max z: 0.993744 Cardioid r = 1 + cos(q) z = 1 + x/r - r Drawing Limits: (-2, -2) - (2, 2) Min z: -2.3, Max z: 1.99374 Pascal's Rose r2 = cos2(2q) z = (x4 - 2x2y2 + y4)/r4 - r2 Drawing Limits: (-2, -2) - (2, 2) Min z: -6.176, Max z: 0.99996 Three Leaf Limaçon r = cos(3q) z = (4x3/r3 - 3x/r) - r Drawing Limits: (-2, -2) - (2, 2) Min z: -3, Max z: 0.993743 Daisy r2 = cos2(4q) z = ((x8 - 12x6y2 + 38x4y4 - 12x2y6 + y8) / r8) - r2 Drawing Limits: (-2, -2) - (2, 2) Min z: -5.53901, Max z: 0.999956 Checkerboard z = cos(x) + cos(y) Drawing Limits: (-10, -10) - (10, 10) Min z: -1.99981, Max z: 2 Two Dimensional Sampling Function z = (sin(x)/x)(sin(y)/y) Drawing Limits: (-10, -10) - (10, 10) Min z: -0.217229, Max z: 1 Rays z = cos(3q) z = 4x3/r3 - 3x/r Drawing Limits: (-10, -10) - (10, 10) Min z: -1, Max z: 1 Four Petal Daisy r2 = cos2(4q), with odd lobes suppressed z = x/r - r Drawing Limits: (-2, -2) - (2, 2) Min z: -3.3, Max z: 0.993744 Six Leaf Clover r2 = cos2(3q) z = 16x6/r6 - 24x4/r4 + 9x2/r2 - r2 Drawing Limits: (-2, -2) - (2, 2) Min z: -6.1261, Max z: 0.993755 Two Petal Rose r = cos(2q) z = ((x2 - y2) / r2) - r Drawing Limits: (-2, -2) - (2, 2) Min z: -3.3, Max z: 0.993744 Spiral r = q z = tan-1(y/x) - r Drawing Limits: (-2, -2) - (2, 2) Min z: -5.13848, Max z: 3.13479 Butterfly basically, r = versin(5q) with lobe sizes adjusted z = ((4y5 - 4y3x2 + 8yx4) / r5) - (3y3 - 3yx2)/r3 - r Drawing Limits: (-2, -2) - (2, 2) Min z: -5.11643, Max z: 2.86601 Circus Tent a pair of polynomials with 5 roots each z = x5 - 5x3 + 4x - y5 + 5y3 - 4y Drawing Limits: (-2, -2) - (2, 2) Min z: -6.91267, Max z: 6.88453 Two Hyperbolae and a Circle z = (x2 - y2 - 1) (y2 - x2 - 1) (x2 + y2 - 1) Drawing Limits: (-1.5, -1.5) - (1.5, 1.5) Min z: -5.07812, Max z: 1.67009 Radial Hyperbolae and Circle r2 = (x2 - y2 - 1) (y2 - x2 - 1) (x2 + y2 - 1) z = (x2 - y2 - 1) (y2 - x2 - 1) (x2 + y2 - 1) - r2 Drawing Limits: (-1.1, -1.1) - (1.1, 1.1) Min z: -1.42419, Max z: -0.851859 Intersecting Waves basically, y = sin(3x) and x = sin(5y) z = (sin(3x) - y) (sin(5y) - x) Drawing Limits: (-3, -3) - (3, 3) Min z: -9.50629, Max z: 8.48362 Black Hole has only imaginary roots z = x2 - xy + y2 Drawing Limits: (-2, -2) - (2, 2) Min z: 0, Max z: 9.21882 A Lonely Pulse basically, y = sin(x)/x z = 10 - (10sin(x) / x) - y Drawing Limits: (-20, -20) - (20, 20) Min z: -14.931, Max z: 27.1723 Vertical Bars z = 10cos(x) Drawing Limits: (-20, -20) - (20, 20) Min z: -9.99919, Max z: 10 Zig Zag basically, y = cos(x) + x z = 5cos(x) + 2x - y Drawing Limits: (-20, -20) - (20, 20) Min z: -52.8971, Max z: 58.1044