#
# File:
# color5.py
#
# Synopsis:
# Draws a Mandelbrot set.
#
# Category:
# Colors
#
# Author:
# Fred Clare
#
# Date of initial publication:
# February, 2006
#
# Description:
# Using parameters for grid resolution and convergence tolerances,
# this script produces a Mandelbrot set and colors it using
# equally-spaced hues in the HLS color space.
#
# Effects illustrated:
# o Drawing filled polygons in NDC space.
# o Converting HLS color values to RGB.
# o Defining a private color table.
# o Using indexed color.
#
# Output:
# One plot is produced showing the Mandelbrot set created.
#
import Ngl
#
# Function for converting from user space in the
# complex plane to NDC.
#
def user2ndc(x, y):
return 0.4*x+0.8, 0.4*y+0.5
#
# Function for computing the convergence of the
# sequence for the Mandelbrot set.
#
# Arguments:
# z - the original complex value.
# num - the maximum number of iterations allowed.
# tolxm - a tolerance value for computed z's close to the original.
# tollg - a tolerance value for computed z's away from the original.
#
# Return:
# The number of iterations it takes to satisfy the tolerance
# criteria, or the maximum number of iterations.
#
def convg(z, num, tolsm, tollg):
zs = z
z0 = z
for i in xrange(num):
zn = z0*z0 + zs
if ( (abs(zn-z0) < tolsm) or (abs(zn-z0) > tollg) ):
return i
z0 = zn
return num
#
# Given the index of a cell in a grid box
# that has lower left corner (xl,yb) and upper
# right corner (xr,yt), and nx divisions in
# x and ny divisions in y, return the polygon
# bounding that cell.
#
def get_cell(i, j, xl, xr, yb, yt, nx, ny):
delx = (xr-xl)/nx
dely = (yt-yb)/ny
xt = xl+i*delx
yt = yb+j*dely
x = [xt, xt+delx, xt+delx, xt, xt]
y = [yt, yt, yt+dely, yt+dely, yt]
return x,y
#
# Main driver.
#
#
# Set up corner points for the area of the
# complex plane under consideraton.
#
xl, xr, yb, yt = -2.00, 0.50, -1.25, 1.25
#
# Specify how many divisions in x and y the
# area above is to have. Increasing these
# numbers will produce a plot with finer
# detail, at the expense of compute time.
#
nx, ny = 90, 90
#
# Specify the maximum number of iterations for
# the convergence test. Increasing this value
# refines the color table. Since color values
# are assigned to the iteration results, "niter"
# cannot be larger than 255.
#
niter = 101
#
# Open a workstation.
#
wks_type = "png"
wks = Ngl.open_wks(wks_type,"color5")
#
# Define our own color table going around
# all the hues in the HLS color space, starting
# with blue.
#
for k in xrange(0,niter):
h = 360*float(k)/float(niter)
r,g,b = Ngl.hlsrgb(h, 50., 100.)
Ngl.set_color(wks, k, r, g, b)
#
# Create the set and draw the color cells.
#
poly_res = Ngl.Resources()
for j in xrange(ny):
for i in xrange(nx):
x, y = get_cell(i, j, xl, xr, yb, yt, nx, ny)
iter = convg(complex(x[0],y[0]), niter, 0.001, 10000)
poly_res.gsFillColor = iter-1 # iter will be at least one.
for i in xrange(len(x)):
x[i], y[i] = user2ndc(x[i], y[i])
Ngl.polygon_ndc(wks, x, y,poly_res)
Ngl.frame(wks)
Ngl.end()