Friday, September 8, 2017

Funny Scalar Fields (Heat Maps) on a Surface

Heat Map on a Torus

Heat Map on a Torus

Scalar Field on a Torus

Scalar Field on a Möbius Strip

Scalar Field on a Möbius Strip


( Mathematical software used: gnuplot )

Funny Inequalities on a Torus

(1)

(2-1)

(2-2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)
(11)

(12)


( Mathematical software used: gnuplot )

Friday, January 27, 2017

Plotting Slope Fields using Graph

y' = x² + y² - r²  (r = 0, 1, 2, ..., 7)


y' = (x + y)/(x - y)  (method 1)


y' = (x + y)/(x - y)  (method 2)


y' = sin(x)/y + sin(y)/x


y' = cos(x) + cos(y)


y' = cos(x) sqrt(1+x²) + cos(y) sqrt(1+y²)


Download Examples:


( Mathematical software used: Graph )

Saturday, January 7, 2017

A Monster Equation

x² + y² - a[exp(sin³(x-y)) + exp(sin³(-x-y))]² = c
  • x and y are variables.
  • a and c are parameters.


(a = 3, c = 0.5)

Scilab script:

clear;
clf();
xset("wdim",400,400);
xset("fpf"," ");
xset("thickness", 2);
square(-8.2,-8.2,8.2,8.2);

a = 3;
c = 0.5;
function z = fun(x,y)
   z = x^2 + y^2 - a*(exp(sin(x-y)^3) + exp(sin(-x-y)^3))^2 - c;
endfunction
data = linspace(-8.2, 8.2, 2000);

contour2d(data, data, fun, [0,0], style=color("red"), axesflag=0);



(a = -1, c = 24)


(a = -2, c = 50)


( Mathematical software used: Scilab )

Wednesday, December 14, 2016

Five Interlaced Moons

Five Interlaced Crescents


Generalization:

Let A and B be two disks with radii a and b.
The set difference A\B is used to plot the moons 
in the following animations.


Animation parameter: the position of B


Animation parameter: b (the radius of B)


Animation parameter: the position of A


Animation parameter: a (the radius of A)


( Mathematical softwares used: gnuplot, GeoGebra )

Four Interlaced Crescents



A cross pattée!







( Mathematical softwares used: Graph, gnuplot )


Related posts:

Triple Crescent Moon

Triple Crescent Moon Symbol
(Boundary curves: circles)


Boundary curves: superellipses with exponent 2.5


Boundary curves: superellipses with exponent 4


A monster face!


Hi!


Exponents: 1.5, 2, 2.5, 3, 3.5, 4


( Mathematical software used: gnuplot )