I have been working on a project for my math class in which I am creating a Julia set generator. I had finally succeeded in generating it, but when I show the plot and save the image generated there are white lines all over it. They do not line up with x ticks or y ticks. When I view the saved image it had even more white lines. I have been searching to find what these might be, but I have found nothing.
import matplotlib.pyplot as plt
#Set up window with a name and size.
plt.figure("Julia Set Generator by Eric Kapilik", figsize=(7.0,7.0))
#Set Range of axes
plt.xlim([-2,2])
plt.ylim([-2,2])
#Add labels to axes
plt.xlabel("Real Numbers")
plt.ylabel("Imaginary Numbers")
plt.grid(b=False, which = "major", axis = "both")
plt.grid(b=False, which = "minor", axis = "both")
name = input("Save file as... \n")
#Ask for maximum amount of iterations to base colour
#selection off of with fractions.
max = int(input("What is the maximum amount of iterations you wish to run? "))
#Generate an array of colour names to be used to plot points.
#Set seed of array.
colourArray = ["r"]
for colourNum in range (1, max):
#if the place in array is between 0% and 25% then set the colour to red.
#Same method used for other three colours.
if colourNum >= 0 and colourNum <= (max/4):
colourArray.append("r") #red
elif colourNum > (max/4) and colourNum <= (max/2):
colourArray.append("y") #yellow
elif colourNum > (max/2) and colourNum <= ((3*max)/4):
colourArray.append("g") #green
elif colourNum > ((3*max)/4) and colourNum <= max:
colourArray.append("c") #cyan
#Get constant value of which the julia set is based off of.
#The real number component is plotted on the horizontal axis
#of a complex number grid so we will use x.
xConstant = float(input("Enter real number constant component: "))
#The imaginary nuber compenent of a complex number is plotted on the vertical axis,
#so we will use y in our real number grid (for simplicity's sake).
yConstant = float(input("Enter imaginary number constant component: "))
#Title the graph based on the constatn complex number entered.
plt.title(str(xConstant) + " + " + str(yConstant) + "i")
#See the starting coordinates to be tested and conditions
xTest = float(-2)
yTest = float(2)
stop = False
i = 0
xPrevious = xTest
yPrevious = yTest
#Using an escape time algorith, determine the amout of iterations of the recursion
#are needed for the coordinate to be attarcted to infinity.
#Continue doing this while the y value of the coordinate being tested is less
#than or equal to -2.
while yTest >= -2:
#We are following the recursive function of
#f(Z-1) = Z^2 + C
#Where Z is current coordinate, and C is the constant value.
#Reminder: Both Z and C are actually complex numbers but in our case we
#are using them both as real number coordinates on a real number grid.
xCurrent = ((xPrevious**2) - (yPrevious**2)) + xConstant
yCurrent = (2 * xPrevious * yPrevious) + yConstant
#Points that surpass a circle of radius 2 with a centre point at the origin
#are considered to indefinitely escape to infinity.
#So when the radius of the recursive coordinate based off of the tested coordinate
#becomes greater or equal to two we know it will be attaracted to infinity.
radius = xCurrent**2 + yCurrent**2
#"Is the point an escapee?"
if radius >= 2:
#Since the point has been defined as one that esacpes to infintity
#it is considered an escapee, so set that to true.
escapee = True
#"Is the point a prisoner?"
if i == max:
#The point is considered a prisoner if max iterations is reached and
#the point is still within the circle of radius 2.
#The testeed point will be considered a prisoner based off of the amount
#of iterations we selected, it is possible that with more iterations
#that we would find this to be an escapee.
prisoner = True
#If we have not defined what kind of point this is yet, then go to the next
#iteration of the recursion. i is the number of iterations completed for
#the test point.
if escapee == False and prisoner == False:
i = i + 1
#Out with the old, in with the new. Set the current points to the previous
#points for the next iteration.
xPrevious = xCurrent
yPrevious= yCurrent
#If, however, we have defined the point, then colour it based off of
#the amount of iterations using the array of colours generated at the
#beginning to select the colour.
if escapee == True or prisoner == True:
#This sets the black points that are prisoners, this is the body
#of the julia set.
if i == max:
colourPoint = "k,"
else:
#Colour the point and concatenate a ",", which means to plot this point
#as a pixel.
colourPoint = colourArray[i] + ","
#Plot the point! (Most satisfying part)
plt.plot(xTest, yTest, colourPoint)
#Determine the percentage finished, to give user an idea of how the
#renderig is going. (Not nessecary, but appreciable)
percent = int(((yTest-2)/4) * (-100))
print(str(percent) + "%")
#After setting a colour and plotting the point, jump to the next test coordinate.
#Once the end of the line is reached, jump down one.
if xTest >= 2:
xTest = -2
yTest = yTest - 0.01
else:
xTest= xTest + 0.01
#Reset the starting conditions.
i = 0
escapee = False
prisoner = False
xPrevious = xTest
yPrevious = yTest
#Show the beauty.
print("100%")
print("Wait for matplotlib to finish things up...\nWill take a minute...")
plt.show()
plt.savefig(name)
Saved image, with even more white lines.
Any suggestions are massively appreciated. Thanks in advanced,
