helix

silviana amethyst

Equation ¶

\[ 6x^2-2x^4 = y^2z^2 \]

Properties: ¶

degree 4
two singular curves, both lines, being the \(y\) and \(z\) axes. They intersect at a singular point at the origin.

Some story ¶

I love this surface, I think it is one of my favorites so far. I took a risk on Helix, printing it large without internal supports, before any trial runs. I feel like I am getting good enough at printing that I can take some risks like this – and it paid off. It came out beautifully, in 33.5 hours of printing. I reduced the speed to 2000mm/minute to help ensure the risky regions would bridge well.

Sphere of radius 5, random projection.

Bertini_real input files ¶

input

CONFIG
randomseed: 2;
tracktype: 1;
securitylevel:1;
sharpendigits: 80;
endpointfinitethreshold: 1e12;
condnumthreshold: 1e300;
odepredictor: 8;
finaltol: 1e-18;
numsamplepoints: 16;
endgamenum: 2;
maxstepsbeforenewton: 0;
maxnewtonits: 1;
END;
INPUT

variable_group x, y, z;
function f;
f = 6*x^2 - 2*x^4 - y^2*z^2;
END;