Some simple formulas

Frm file containing all formulas in Fractint format.

4 spirals
x=.004*x+y; 
y=(-1./y - y)/x;
Other representations

Chaotic oval
x = x/y -x;
y = x*x - 0.24;
Other representations

Chaotic shell
x = x*y + 0.357057*x -y; 
y = x + y;
Other representationsGallery images:1,2

Circle
x=-0.999776*y; 
y=x+0.1*y;
Other representations

Circle of circles
 x=y;
y=-0.288/y +0.5*y - x;
Other representations

Diagonal
x=.001*y+y; 
y=x;
Other representations

E shape
x=-y;
y=x+y+1/y;
Other representations

Fractured window
x= -.127219  + y
y = .02246817*y/x -x
Gallery images:1

Hammer
x = 0.37363*x*x-1.182076*x+y
y = -x + 1.33173
Gallery images:1,2

Hexagon
x=-0.999776*y; 
y=x+y;
Other representations

Insect
x=y;
y=y*y+x+y;
Other representations

Knot
x=-y; 
y=x*x*x-x-y;
Other representationsGallery images:1,2

Mantle
x = y - 0.614927
y = x*x - y
Gallery images:1

Mask
x = 0.538999*x-y
y = 1.629151*x -x*x
Gallery images:1

Matrix
c0 = 0.7121
d0 = 0.336315
x = c0 - y
y = d0/(x*x)+x
Gallery images:1

Pentagon
x=x*0.6 -y;  
y=0.1*x*y +x;
Other representations

Sleeping man
a = 0.009556639
b = 0.001269858
c = 0.7225745
d = 1
x = x/(a*x*y + b*(y/x) +c/x + x + d) - y + x
y = x
Gallery images:1,2,3,4

Spiral
x = a*y 
y = x+b*y
Other representationsGallery images:1
By changing a and b you can get many kinds of spirals.Note that the square and hexagon formula are a special case of this formula.

Square
x=-0.999776*y; 
y=x-y;
Other representationsGallery images:1

Triangle
x=-0.999776*y;  
y=x-y;
Other representations

Venus
a = -0.00001
b = -0.240934
c = 0.096143
x = y + a*y*y
y = b*y*y -x +c
Gallery images:1

Vine
x = -y;
y = -2*x*x*y+2*y;
Other representationsGallery images:1