# 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 representations Gallery 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 representations Gallery 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 representations Gallery 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 representations Gallery 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 representations Gallery images:1