Making Art with Mathematical Equations, Inequalities and Functions (Mappings, Transformations)

## Thursday, July 28, 2011

## Sunday, July 24, 2011

## Wednesday, July 20, 2011

## Tuesday, July 19, 2011

### UDAV example: plotting implicit curves (level curves)

In this example, we will plot the

the equation fun(x,y) = 0.

fun(x,y) =

setsize 400 400

plotfactor 1

xrange -2 2

yrange -2 2

new fun 512 512

list v 0

fill fun '(x*x+y*y-3)*sqrt(x*x+y*y) + 0.75 + 0.5*sin(4*sqrt(x*x+y*y))*cos(5*atan(y/abs(x))) - sin(5*atan(y/abs(x)))'

cont v fun 'r'

The following image shows the result:

**implicit curve**(**,**__level curve__**) defined by**__contour line__the equation fun(x,y) = 0.

fun(x,y) =

**MGL script:**setsize 400 400

plotfactor 1

xrange -2 2

yrange -2 2

new fun 512 512

list v 0

fill fun '(x*x+y*y-3)*sqrt(x*x+y*y) + 0.75 + 0.5*sin(4*sqrt(x*x+y*y))*cos(5*atan(y/abs(x))) - sin(5*atan(y/abs(x)))'

cont v fun 'r'

The following image shows the result:

### Gnuplot example: plotting implicit curves (level curves)

In this example, we will plot the

the equation fun(x,y) = 0.

fun(x,y) =

fun(x,y) = (x*x+y*y-3)*sqrt(x*x+y*y) + 0.75 \

+ sin(8*sqrt(x*x+y*y))*cos(6*atan(y/abs(x))) - 0.75*sin(5*atan(y/abs(x)))

set xrange [-2:2]

set yrange [-2:2]

set size ratio -1

set samples 512

set isosamples 512

set contour base

set cntrparam levels discrete 0

unset key

unset xtics

unset ytics

unset border

unset surface

set table 'curve.dat'

splot fun(x,y)

unset table

plot 'curve.dat' w l lw 1.5 lc rgb "red"

The result plot:

**implicit curve**(**,**__level curve__**) defined by**__contour line__the equation fun(x,y) = 0.

fun(x,y) =

**gnuplot script:**fun(x,y) = (x*x+y*y-3)*sqrt(x*x+y*y) + 0.75 \

+ sin(8*sqrt(x*x+y*y))*cos(6*atan(y/abs(x))) - 0.75*sin(5*atan(y/abs(x)))

set xrange [-2:2]

set yrange [-2:2]

set size ratio -1

set samples 512

set isosamples 512

set contour base

set cntrparam levels discrete 0

unset key

unset xtics

unset ytics

unset border

unset surface

set table 'curve.dat'

splot fun(x,y)

unset table

plot 'curve.dat' w l lw 1.5 lc rgb "red"

The result plot:

**Related posts:**

## Monday, July 18, 2011

## Saturday, July 16, 2011

## Monday, July 11, 2011

## Sunday, July 3, 2011

### Flying Mallet (飛天神槌)

( Mathematical software used: Graph )

## Saturday, July 2, 2011

### Funny Equations - animations of curves

## Friday, July 1, 2011

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