# Math Art Editor >> Gallery

## Function 1

Re(f(x,y)) =

Im(f(x,y)) =

Parameter

a1[0] (0:0.1:10), a1[1] (0:0.1:10), a1[2] (0:0.1:10),

a1[3] (-1:0.01:1), a1[4] (-5:0.1:5), a1[5] (0:0.1:100),

a1[6] (0:0.1:10), a1[7] (0:0.1:10),

a1[8] (-2:0.01:2), a1[9] (-2:0.01:2)

## Function 2

Re(f(x,y)) =

Im(f(x,y)) =

Parameter

b1[0] (0:0.1:10), b1[1] (0:0.1:10), b1[2] (0:0.1:10),

b1[3] (-1:0.01:1), b1[4] (-5:0.1:5), b1[5] (0:0.1:100),

b1[6] (0:0.1:10), b1[7] (0:0.1:10),

b1[8] (-2:0.01:2), b1[9] (-2:0.01:2)

## Domain Colouring

The color wheel method is a method to graphically represent complex functions. Complex functions represent the two-dimensional complex plane in turn, the real and imaginary values. The color circle method used amount r = |f(z)| and angle φ the complex function value f(z) around the display color of the function value set. According to r and φ the function value is selected the color from the color wheel. The amount defines the saturation and modulo is mapped to intervals . The first interval is 0 .. 1 then follow the intervals ( 1 .. e] , (e. .. e 2 ] , (e 2 ... e 3 ], etc. the color is defined by the angle and in 6 color zones starting with split blue from 0° to 60° and ending with green from 300° to 360°. the method is designed to that the function values ​​are close together are also displayed similar color. mapping the sums on intervals of the power of e corresponds to a logarithmic representation.

## Colour Wheel

A compilation of a color wheel can be put together from different points depending on which state of affairs is to be visualized. The basis for the color circle the perception of similar colors. Leaving subjects with normal color pattern according to the sensation on similarity sort, which hues are usually brought in the same order. Beginning and end of the series are around so similar that the series can be closed to form a circle.

## Complex function plot

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The first two plots show the two complex functions with the color wheel method. The third plot shows the result function corresponding to the selected operation (+, -, * or /). The complex functions are given in the following form:

$f\left(z\right)=\mathfrak{Re}\left(f\left(x,y\right)\right)+i\mathfrak{Im}\left(f\left(x,y\right)\right)$

$\text{with}\phantom{\rule{1em}{0ex}}z\phantom{\rule{0.5em}{0ex}}\in \phantom{\rule{0.5em}{0ex}}\mathbb{C}\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\mathrm{x, y}\phantom{\rule{0.5em}{0ex}}\in \phantom{\rule{0.5em}{0ex}}\mathbb{R}\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}z=x+i\phantom{\rule{0.3em}{0ex}}y$

In the definition of the functions can be used the parameter a1[0]...a1[9] and b1[0]...b1[9]. The parameter can be adjusted by the slider. The parameter range is annotated at the slider in the form (start value:step:end value).

The following term can be used in the definition of the functions:

Constants

NameDescription
LN2Natural logarithm of 2
LN10Natural logarithm of 10
LOG2EBase 2 logarithm of EULER
LOG10EBase 10 logarithm of EULER
PIRatio of the circumference of a circle to its diameter
SQRT1_2Square root of 1/2
SQRT2Square root of 2

Trigonometric Functions

FunctionDescription
sin(x)sine of x
cos(x)Cosine of x
tan(x)Tangent of x
asin(x)arcsine
acos(x)arccosine of x
atan(x)arctangent of x
atan2(y, x)Returns the arctangent of the quotient of its arguments.
cosh(x)Hyperbolic cosine of x
sinh(x)Hyperbolic sine of x

Logarithm and Exponential

FunctionDescription
pow(b, e)e to the b
sqrt(x)Square root of x
exp(x)EULER to the x
log(x), ln(x)Natural logarithm
log(x, b)Logarithm to base b
log2(x), lb(x)Logarithm to base 2
log10(x), ld(x)Logarithm to base 10

More functions

FunctionDescription
ceil(x)Get smallest integer n with n > x.
abs(x)Absolute value of x
max(a, b, c, ...)Maximum value of all given values.
min(a, b, c, ...)Minimum value of all given values.
random(max = 1)Generate a random number between 0 and max.
round(v)Returns the value of a number rounded to the nearest integer.
floor(x)Returns the biggest integer n with n < x.
factorial(n)Calculates n!
trunc(v, p = 0)Truncate v after the p-th decimal.

## Hue

The hue is selected according to the angle.

## Lightness

The brightness is determined according to the following diagram.

In the interval [0,0.5) applies val = a1 * k + b1

In the interval [0.5,1) applies val = a2 * k + b2

It is: min ≤ val ≤ max

## Saturation

The saturation is determined according to the following diagram.

In the interval [0,0.5) applies sat = a1 * k + b1

In the interval [0.5,1) applies sat = a2 * k + b2

It is: min ≤ sat ≤ max