Cosine Star (1) (餘弦星 1)

( Softwares used: Graph, gnuplot, Ulead GIF Animator )

Sine Star (1) (正弦星 1)

( Softwares used: Graph, gnuplot, Ulead GIF Animator )

Alien Puppy (2) (外星小狗 2)

( Mathematical softwares used: gnuplot, UDAV )

Grandpapa (老爺爺)

( Mathematical software used: gnuplot )

Little Pharaoh (小小法老王)

( Mathematical software used: Graph )

Starflakes

A five-pointed star ( ☆ ) can be expressed as an equation constructed from five lines. The above animation consists of 100 frames. Each frame image is the graph of an inequality constructed from five collections of infinitely many parallel lines.


( Softwares used: gnuplot, Ulead GIF Animator )

Antlerman (2): The Antlerman Sequence (鹿角超人 2)

The antlerman sequence is an iterative sequence of equations.

A₀(x,y) = 0:

 (Click on the image for a larger view.)
A₀ is derived from one of the Funny Equations.

A₁(x,y) = 0:

Colored plots of z = A₁(x,y): Antlerman (1)

A₂(x,y) = 0:

(Click on the image for a larger view.)

A₃(x,y) = 0:

( Softwares used: gnuplot, Ulead GIF Animator )

 Related posts:

•  Antlerman (1)

Flag of the United States - plotting contour maps using gnuplot (graphing inequalities using Graph)

gnuplot script:

a = 1.0
b = 1.9
c = 7.0/13.0
d = 0.76
f = 7.0/130.0
g = 19.0/300.0
k = 0.0308
l = 1.0/13.0

star(x,y) = \
( (5+sqrt(5))*abs(x) - sqrt(10-2*sqrt(5))*(y+4*k) \
   + abs( (5+3*sqrt(5))*abs(x) + sqrt(50+10*sqrt(5))*y ) \
   + abs( 2*sqrt(5)*abs(x) - 2*sqrt(25+10*sqrt(5))*y ) \
   - abs( (5-3*sqrt(5))*abs(x) - sqrt(50-10*sqrt(5))*y \
             + abs( (5+3*sqrt(5))*abs(x) + sqrt(50+10*sqrt(5))*y ) \
             - abs( 2*sqrt(5)*abs(x) - 2*sqrt(25+10*sqrt(5))*y ) ) ) / k

set xrange [0:b]
set yrange [-a:0]

fun(x,y) = \
( x < d && y > -c \
   && star( x - g, y + f ) > 0 \
   && star( x - 3*g, y + f ) > 0 \
   && star( x - 5*g, y + f ) > 0 \
   && star( x - 7*g, y + f ) > 0 \
   && star( x - 9*g, y + f ) > 0 \
   && star( x - 11*g, y + f ) > 0 \
   && star( x - g, y + 3*f ) > 0 \
   && star( x - 3*g, y + 3*f ) > 0 \
   && star( x - 5*g, y + 3*f ) > 0 \
   && star( x - 7*g, y + 3*f ) > 0 \
   && star( x - 9*g, y + 3*f ) > 0 \
   && star( x - 11*g, y + 3*f ) > 0 \
   && star( x - g, y + 5*f ) > 0 \
   && star( x - 3*g, y + 5*f ) > 0 \
   && star( x - 5*g, y + 5*f ) > 0 \
   && star( x - 7*g, y + 5*f ) > 0 \
   && star( x - 9*g, y + 5*f ) > 0 \
   && star( x - 11*g, y + 5*f ) > 0 \
   && star( x - g, y + 7*f ) > 0 \
   && star( x - 3*g, y + 7*f ) > 0 \
   && star( x - 5*g, y + 7*f ) > 0 \
   && star( x - 7*g, y + 7*f ) > 0 \
   && star( x - 9*g, y + 7*f ) > 0 \
   && star( x - 11*g, y + 7*f ) > 0 \
   && star( x - g, y + 9*f ) > 0 \
   && star( x - 3*g, y + 9*f ) > 0 \
   && star( x - 5*g, y + 9*f ) > 0 \
   && star( x - 7*g, y + 9*f ) > 0 \
   && star( x - 9*g, y + 9*f ) > 0 \
   && star( x - 11*g, y + 9*f ) > 0 \
   && star( x - 2*g, y + 2*f ) > 0 \
   && star( x - 4*g, y + 2*f ) > 0 \
   && star( x - 6*g, y + 2*f ) > 0 \
   && star( x - 8*g, y + 2*f ) > 0 \
   && star( x - 10*g, y + 2*f ) > 0 \
   && star( x - 2*g, y + 4*f ) > 0 \
   && star( x - 4*g, y + 4*f ) > 0 \
   && star( x - 6*g, y + 4*f ) > 0 \
   && star( x - 8*g, y + 4*f ) > 0 \
   && star( x - 10*g, y + 4*f ) > 0 \
   && star( x - 2*g, y + 6*f ) > 0 \
   && star( x - 4*g, y + 6*f ) > 0 \
   && star( x - 6*g, y + 6*f ) > 0 \
   && star( x - 8*g, y + 6*f ) > 0 \
   && star( x - 10*g, y + 6*f ) > 0 \
   && star( x - 2*g, y + 8*f ) > 0 \
   && star( x - 4*g, y + 8*f ) > 0 \
   && star( x - 6*g, y + 8*f ) > 0 \
   && star( x - 8*g, y + 8*f ) > 0 \
   && star( x - 10*g, y + 8*f ) > 0 ) \
? 2 : ( (x > d || y < -c) && sin(y*pi/l) < 0 ) ? 0 : 1

set pm3d map
unset colorbox
set palette model RGB defined (0 '#BB133E', 1 'white', 2 '#002664')

set size ratio -1
set samples 760, 400
set isosamples 760, 400

set bmargin 0
set lmargin 0
set rmargin 0
set tmargin 0

unset key
unset xtics
unset ytics
unset border

splot fun(x,y)


Graph example:

The grf file download page: Flag of the United States.

Sacred Insects (神聖昆蟲)

( Mathematical software used: UDAV )

Tribal Warrior (部落勇士)

( Mathematical software used: UDAV )