Fun math art (pictures) - benice equation: Alien

Showing posts with label Alien. Show all posts

Sunday, May 29, 2016

Alien Children

The main equation is a branch of the polar equation

r³ - 3r = a(sinθ - abs(cosθ)), where a = 1.4

Its rectangular equation is

(x² + y² - 3)(x² + y²) = 1.4(y - abs(x))

The main equation is a branch of the polar equation

r³ - 3r + 3 = a(e^sinθ + abs(sinθ)^e), where a = 1.45

Its rectangular equation is

(x² + y² - 3) sqrt(x² + y²) + 3

= 1.45(e^(y/sqrt(x² + y²)) + abs(y/sqrt(x² + y²))^e)

( Mathematical software used: gnuplot )

Thursday, August 22, 2013

UFO Monster (3) (幽浮怪物 3)

The original graph

( Mathematical software used: gnuplot )

Friday, August 2, 2013

Friday, July 12, 2013

Alien Rebirth Memorial Statue (外星人重生紀念雕像)

( Mathematical software used: Graph )

Tuesday, July 2, 2013

Sunday, November 4, 2012

Sunday, September 30, 2012

Gnuplot example: Math Invaders - Remember Space Invaders and Galaxian?

This is a parameter animation (plotted upside down) for the modified Thomae function:

gnuplot script:

d = 0.001
m = 250
f(n,k,x) = k > m ? 3.2 : ( abs(k*x - int(k*x)) < d ? \
3.2-(1+0.1*n*n)/(k*k-abs(k*x)) : f(n,k+1,x) )
set xrange [-1.6:1.6]
set yrange [0:3.2]
set size ratio -1
set samples 10000
unset key
unset xtics
unset ytics
unset border
set bmargin 0
set lmargin 0
set rmargin 0
set tmargin 0
set term gif size 400, 400 animate background rgb "black"
set output "C:\math_invaders.gif"
set pointsize 0.5
do for [i=0:150]{
plot f(i,1,sin(x)) with points pt 11 lc rgb "white"
}
set output

Note that we set less samples(10000). By incresing samples to 200000,
we can obtain a more accurate (but less fun) picture.