Cat Girl

Equations:

Contour lines:
(16*x^4 + y^4 - 16*x^2*y - 0.1) * (x^2 + (y - 0.5)^2 - 1) = 0.25
(16*x^4 + y^4 - 16*x^2*y - 0.1) * (x^2 + (y - 0.5)^2 - 1) = -2.5

Eyes:
(abs(x) - 0.5)^2 + (y - 0.75)^2 = 0.25^2

Pupils:
(abs(x) - 0.5)^2 + (y - 0.7)^2 = 0.06^2

Nose:
x^2 + 0.75*(y - 0.1)^2 = 0.1^2

Mouth:
x^2 + 8*(y + 0.25)^2 = 0.1^2

Whiskers:
y = sign(x)*(x - 0.55*asin(x)) - 0.025
y = sign(x)*(0.9*x - 0.8*asin(0.9*x)) - 0.025
y = sign(x)*(1.2*x - 1.1*asin(1.2*x)) - 0.025

( Mathematical software used: Graph, GeoGebra )

Spiral Starfish - a logarithmic spiral pentaskelion (螺旋海星)

A pentaskelion with five logarithmic spirals r(θ) = a*exp(b*θ),

b ~ 0.30635 (same as that of the golden spiral).

b = 0.25

b = 0.5

b = golden ratio ~ 0.618

( Mathematical software used: gnuplot )

Symbiosis (共生)

Hey, that's my tail!

The original graph.

( Mathematical software used: gnuplot )

Featherless Bird (無毛怪鳥)

( Mathematical software used: Graph )

Alien Fish (外星魚)

( Mathematical software used: UDAV )

A Pair of Penguins (一對企鵝)

The original graph (of equation)

( Mathematical software used: gnuplot )

Duck Man (鴨子人)

The original graph (of equation)

( Mathematical software used: gnuplot )

Flying Pig (飛天豬)

( Mathematical software used: gnuplot )

Ghost Bat and Evil Owl (鬼蝙蝠與邪惡貓頭鷹)

( Mathematical software used: gnuplot )

Birdies and Doggies (小鳥與小狗)

( Mathematical software used: UDAV )

Insect-like Spirograph

( Mathematical software used: GeoGebra )

Monkey Faces (猴子臉)

( Mathematical softwares used: gnuplot, UDAV )

Alien Puppy (2) (外星小狗 2)

( Mathematical softwares used: gnuplot, UDAV )

Sacred Insects (神聖昆蟲)

( Mathematical software used: UDAV )

Cai Shen Cow (財神牛)

Note: Cai Shen (財神 or 財神爺) is the Chinese god of prosperity.

( Mathematical software used: UDAV )

Owl Scout (貓頭鷹偵察兵)

( Mathematical software used: UDAV )


Link:
Another math-generated owl picture by Maths is smART.
-- It's a 2D plot which looks like a 3D mesh plot. Very interesting!

Monster Cow (怪牛)

( Mathematical software used: gnuplot )

Kung Fu Dog (功夫小黃)

( Mathematical software used: UDAV )

Alien Puppy (1) (外星小狗 1)

( Softwares used: gnuplot, UDAV )

Little Mouse (小老鼠)

1. The mouse in the original graph of the inequality fun(x,y) > 0 has no mouth.

2. Add a circle ( mouth(x,y) = 0 ) as the border line of the mouth.
    Graph fun(x,y) * mouth(x,y) > 0.

3. Add the boundary curves of the inequality regions which will be colored black or white.

4. The red and green meshed regions will be colored black and white, respectively.

5. Color the inequality regions black or white.

6. The finished result.

( Softwares used: gnuplot, Graph )