Visualizing complex-valued functions with Matplotlib and Mayavi Domain coloring method
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The study of complex-valued functions is a difficult chapter of mathematics for most students.\n",
"Usually textbooks do not show up any figure to visualize in some way such functions."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"When studying real functions of one or two variables, an intuitive grasp of some properties one acquires looking at their graphs.\n",
"Unlike real functions of one or two variables, whose graphs are curves in $\\mathbb{R}^2$, respectively\n",
" surfaces in $\\mathbb{R}^3$, the graph of a complex function, $f:\\mathbb{C}\\to\\mathbb{C}$, lies in $\\mathbb{R}^4$. \n",
"Visualization in four dimensions is a difficult task and the method employed depends on the \"geometry\" of the object to be visualized.\n",
"\n",
"Fortunately, the development of cylindrical color models, such as [HSL and HSV](http://en.wikipedia.org/wiki/HSL_and_HSV), and the possibility to express the values $f(z)$ of a complex function in polar coordinates, $f(z)=|f(z)|\\exp(i \\arg(f(z))$, led to the design of a fruitful technique of visualization of the values of a complex function through a color-coding method. This method is called domain coloring. \n",
"\n",
"A list of references dedicated to visualization of complex functions, as well as of the software implementations of different methods of visualization can be found in [Notices of AMS](http://www.ams.org/notices/201106/rtx110600768p.pdf) and on [Hans Lundmark's complex analysis pages](http://users.mai.liu.se/hanlu09/complex/).\n",
"\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In order to understand the basic idea behind domain coloring we describe the RGB and HSV color model."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### RGB and HSV color model"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The RGB (Red, Green, Blue) is the basic color space. Its geometrical model is the unit cube. Each color is represented as a triple $(r,g,b)$ of real numbers in $[0,1]$, where $r,g,b $ are quantities \n",
"of the primary colors (red, green and blue) contained by that color. \n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import Image\n",
"Image(url='http://www.blackice.com/images/RGB_Cube.jpg')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Computers treat colors in RGB format. However in applications it is much more appropriate to use the HSV color model, because colors in this space are specified in the same way the humans perceive the color, namely giving the hue, saturation and brightness.\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Image(filename='Imags/HSV.png')# a resized image of this one\n",
" #http://en.wikipedia.org/wiki/File:HSV_color_solid_cylinder_alpha_lowgamma.png"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The HSV model is represented by a solid cylinder having the radius $1$, and height 1. $H$ is the hue, $S$, saturation, and $V$ represents the brightness.\n",
"\n",
"Sectioning this cylinder with a plane perpendicular to its vertical axis, at the height $V=v$, one gets a color wheel whose complex parameterization is\n",
" $z=Se^{2\\pi i H}$.\n",
"\n",
"As hue $H$ varies from 0 to 1, the corresponding colors vary in this color wheel such that at $2\\pi H$, with $H\\in\\{0, 1/6, 1/3, 1/2, 2/3, 5/6, 1\\}$ are located respectively the colors red, yellow, green, cyan, blue, magenta, and red again (see the next image).\n",
"\n",
"Saturation represents the purity of colors. For $S=1$ all colors are pure (do not contain white). As $S$ decreases the colors look more fade.\n",
"\n",
"The brightness increases from zero to 1. At $V=0$, all colours look dark.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The images below illustrate the color wheels of brightness $V=1$, respectively $V=0.5$.\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/jpeg": 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\n",
"text/plain": [
""
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Image(filename='Imags/ColorWheelV1.jpg') "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/jpeg": 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\n",
"text/plain": [
""
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Image(filename='Imags/ColorWheelV05.jpg')"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"from matplotlib.colors import hsv_to_rgb"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us get new insights into the HSV model. \n",
"\n",
"In order to see how the color brightness varies in a cylindrical surface of constant saturation, we generate the colors\n",
"in a rectangle obtained by cutting that cylindrical surface along the generatrice of angular coordinate, $H=0$:"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
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