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Title: Draw the Mandelbrot Set in Python – Real Python

Open Graph Title: Draw the Mandelbrot Set in Python – Real Python

Description: In this tutorial, you'll visualize the famous Mandelbrot set using Python's Matplotlib and Pillow libraries. You'll learn how to draw the fractal in black and white, grayscale, and color.

Open Graph Description: In this tutorial, you'll visualize the famous Mandelbrot set using Python's Matplotlib and Pillow libraries. You'll learn how to draw the fractal in black and white, grayscale, and color.

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Table of Contentshttps://realpython.com/mandelbrot-set-python/#toc
Understanding the Mandelbrot Sethttps://realpython.com/mandelbrot-set-python/#understanding-the-mandelbrot-set
The Icon of Fractal Geometryhttps://realpython.com/mandelbrot-set-python/#the-icon-of-fractal-geometry
The Boundary of Iterative Stabilityhttps://realpython.com/mandelbrot-set-python/#the-boundary-of-iterative-stability
The Map of Julia Setshttps://realpython.com/mandelbrot-set-python/#the-map-of-julia-sets
Plotting the Mandelbrot Set Using Python’s Matplotlibhttps://realpython.com/mandelbrot-set-python/#plotting-the-mandelbrot-set-using-pythons-matplotlib
Low-Resolution Scatter Plothttps://realpython.com/mandelbrot-set-python/#low-resolution-scatter-plot
High-Resolution Black-and-White Visualizationhttps://realpython.com/mandelbrot-set-python/#high-resolution-black-and-white-visualization
Drawing the Mandelbrot Set With Pillowhttps://realpython.com/mandelbrot-set-python/#drawing-the-mandelbrot-set-with-pillow
Finding Convergent Elements of the Sethttps://realpython.com/mandelbrot-set-python/#finding-convergent-elements-of-the-set
Measuring Divergence With the Escape Counthttps://realpython.com/mandelbrot-set-python/#measuring-divergence-with-the-escape-count
Smoothing Out the Banding Artifactshttps://realpython.com/mandelbrot-set-python/#smoothing-out-the-banding-artifacts
Translating Between Set Elements and Pixelshttps://realpython.com/mandelbrot-set-python/#translating-between-set-elements-and-pixels
Making an Artistic Representation of the Mandelbrot Sethttps://realpython.com/mandelbrot-set-python/#making-an-artistic-representation-of-the-mandelbrot-set
Color Palettehttps://realpython.com/mandelbrot-set-python/#color-palette
Color Gradienthttps://realpython.com/mandelbrot-set-python/#color-gradient
Color Modelhttps://realpython.com/mandelbrot-set-python/#color-model
Conclusionhttps://realpython.com/mandelbrot-set-python/#conclusion
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algorithmshttps://realpython.com/tutorials/algorithms/
data-vizhttps://realpython.com/tutorials/data-viz/
numpyhttps://realpython.com/tutorials/numpy/
Understanding the Mandelbrot Sethttps://realpython.com/mandelbrot-set-python/#understanding-the-mandelbrot-set
The Icon of Fractal Geometryhttps://realpython.com/mandelbrot-set-python/#the-icon-of-fractal-geometry
The Boundary of Iterative Stabilityhttps://realpython.com/mandelbrot-set-python/#the-boundary-of-iterative-stability
The Map of Julia Setshttps://realpython.com/mandelbrot-set-python/#the-map-of-julia-sets
Plotting the Mandelbrot Set Using Python’s Matplotlibhttps://realpython.com/mandelbrot-set-python/#plotting-the-mandelbrot-set-using-pythons-matplotlib
Low-Resolution Scatter Plothttps://realpython.com/mandelbrot-set-python/#low-resolution-scatter-plot
High-Resolution Black-and-White Visualizationhttps://realpython.com/mandelbrot-set-python/#high-resolution-black-and-white-visualization
Drawing the Mandelbrot Set With Pillowhttps://realpython.com/mandelbrot-set-python/#drawing-the-mandelbrot-set-with-pillow
Finding Convergent Elements of the Sethttps://realpython.com/mandelbrot-set-python/#finding-convergent-elements-of-the-set
Measuring Divergence With the Escape Counthttps://realpython.com/mandelbrot-set-python/#measuring-divergence-with-the-escape-count
Smoothing Out the Banding Artifactshttps://realpython.com/mandelbrot-set-python/#smoothing-out-the-banding-artifacts
Translating Between Set Elements and Pixelshttps://realpython.com/mandelbrot-set-python/#translating-between-set-elements-and-pixels
Making an Artistic Representation of the Mandelbrot Sethttps://realpython.com/mandelbrot-set-python/#making-an-artistic-representation-of-the-mandelbrot-set
Color Palettehttps://realpython.com/mandelbrot-set-python/#color-palette
Color Gradienthttps://realpython.com/mandelbrot-set-python/#color-gradient
Color Modelhttps://realpython.com/mandelbrot-set-python/#color-model
Conclusionhttps://realpython.com/mandelbrot-set-python/#conclusion
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complex numbers in Pythonhttps://realpython.com/python-complex-numbers/
object-oriented programminghttps://realpython.com/python3-object-oriented-programming/
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complex numbershttps://en.wikipedia.org/wiki/Complex_number
logarithmshttps://en.wikipedia.org/wiki/Logarithm
set theoryhttps://en.wikipedia.org/wiki/Set_theory
iterated functionshttps://en.wikipedia.org/wiki/Iterated_function
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complex planehttps://en.wikipedia.org/wiki/Complex_plane
fractalhttps://en.wikipedia.org/wiki/Fractal
https://files.realpython.com/media/wikimedia_Mandel_zoom_00_mandelbrot_set.54d99530ad68.jpg
Benoît Mandelbrothttps://en.wikipedia.org/wiki/Benoit_Mandelbrot
self-similarhttps://en.wikipedia.org/wiki/Self-similarity
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recursionhttps://realpython.com/python-thinking-recursively/
https://realpython.com/mandelbrot-set-python/#the-boundary-of-iterative-stability
boundedhttps://en.wikipedia.org/wiki/Bounded_function
generator objecthttps://realpython.com/introduction-to-python-generators/
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lazy evaluationhttps://en.wikipedia.org/wiki/Lazy_evaluation
maximum recursion limithttps://realpython.com/python-recursion/#recursion-in-python
https://files.realpython.com/media/plot_mandelbrot_with_circle.ad8b99d3ee01.png
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Gaston Juliahttps://en.wikipedia.org/wiki/Gaston_Julia
default argument valuehttps://realpython.com/python-optional-arguments/
connectedhttps://en.wikipedia.org/wiki/Connected_space
Fatou setshttps://en.wikipedia.org/wiki/Fatou_set
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np.linspace()https://realpython.com/np-linspace-numpy/
matrixhttps://en.wikipedia.org/wiki/Matrix_(mathematics)
vectorizationhttps://realpython.com/numpy-array-programming/#what-is-vectorization
broadcastinghttps://realpython.com/numpy-array-programming/#broadcasting
maskhttps://realpython.com/numpy-tutorial/#masking-and-filtering
standard error stream (stderr)https://en.wikipedia.org/wiki/Standard_streams#Standard_error_(stderr)
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C source codehttps://github.com/python-pillow/Pillow/blob/e122e8f3a663efe0fcdf604f189b5695ef9bf227/src/libImaging/Effects.c#L23
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Misiurewicz pointhttps://en.wikipedia.org/wiki/Misiurewicz_point
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algorithms for plotting the Mandelbrot sethttps://en.wikipedia.org/wiki/Plotting_algorithms_for_the_Mandelbrot_set
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color palettehttps://en.wikipedia.org/wiki/Palette_(computing)
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