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based on the hopalong algorithm by Barry Martin
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presented in the September 1986 Scientific American
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Computer Recreations column by A. K. Dewdney
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algorithm starts on page 15
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from tWrapper import tWrapper
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#import math # must be built-in, this isn't needed for sin and cos ?!
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# wrapper for any additional drawing routines
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# that need to know about each other
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class turtleCoat(tWrapper):
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def hopalong(self, a=30.0, b=1.0, c=0.9, iterations=100000,
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xOffset=300.0, yOffset=300.0, scale=10.0):
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# other interesting values for a, b, and c are
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a = 73, b = 2.6, c = 25
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a = -200, b = .1, c = -80
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a = .4, b = 1, c = 0 (try a scale of 100 or 200 on this one)
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a = -3.14, b = .3, c = .3
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colors = ['red', 'orange', 'yellow', 'white', 'green', 'blue', 'purple']
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colorIter = iterations / len(colors)
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#colorIter = iterations / 500
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for i in range(len(colors)):
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#for i in range(colorIter):
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for j in range(colorIter):
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temp = y - self.sign(x) * sqrt(abs(b * x - c))
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self.plot(xOffset + (x * scale), yOffset + (y * scale))
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# the calculation and drawing below take approx. 2/3 the time
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# compared to using plot
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#x2 = xOffset + (x * scale)
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#y2 = yOffset + (y * scale)
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#self.dc.DrawLine(x2, y2, x2 + 1, y2 + 1)
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#def drawMain(dc_local, w, rs=reset, turtleCoat=turtleCoat):
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def drawMain(dc_local, w, turtleCoat=turtleCoat):
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t = turtleCoat(dc_local)
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# chaos1 (Ctrl-1) takes 2.2 seconds versus 7.14 seconds
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# for this chaos1 done as an exec
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t.setBackColor('black')
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a = 73, b = 2.6, c = 25
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a = -200, b = .1, c = -80
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a = .4, b = 1, c = 0 (try a scale of 100 or 200 on this one)
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a = -3.14, b = .3, c = .3
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# beware of doing many iterations on a slow machine
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# 500,000 iterations takes approximately 15 seconds on my AMD 1.2GHz Windows 2000 box
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# with a GeForce 2 video card, so an older machine is likely to take much longer
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# for reference, a similar Java applet I wrote takes under 5 seconds to do 500,000
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# iterations on the same machine using the Sun JDK 1.3 and approximately 1 second
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# using the IBM JDK 1.3
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# if the self.dc.DrawLine ... is used above instead of the plot, drawing takes
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# under 11 seconds and if no drawing is done, just the loop and calculations
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# it takes 3 seconds to do 500,000 iterations
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# some of the difference is likely Python compared to Java
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# but some of it is how screen i/o is done, which is generally the slowest
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# part of any drawing program, especially without any optimizations to the
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# underlying APIs and drivers like DirectX
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# The important point is that it is fast enough.
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# bump this up to 500000 or more iterations to get interesting
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# i set it at 100000 in case someone tried it on a slow machine
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t.hopalong(30.0, 1.0, 0.9, 100000, 300.0, 300.0, 10.0)
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#t.hopalong(73.0, 2.6, 25, 500000, 300.0, 300.0, 5.0)
added
removed
samples/turtle/scripts/hopalong.txt
