Twilight

silviana amethyst

Equation

\[ (z^3-2)^2+(x^2+y^2-3)^3 \]

Properties:

Some story

Twilight, that time when dark and light are indistinguishable.

This surface is difficult to print, as it has a horizontal cusp singularity, which is hard to resolve as an overhang. Cool it!

Bertini_real input files

input

%this is input file for surface `twilight` from Herwig Hauser's gallery.
CONFIG
tracktype: 1;
sharpendigits: 50; %sharpen nonsingular solutions to 50 digits or more using newton's method.
% this helps reduce the chance that two solutions which are supposed to be the same are marked as different.
randomseed: 4; %fix the randomseed to eliminate changes run to run due to randseed.
odepredictor: 8;
endgamenum: 2; %the cauchy endgame
numsamplepoints: 10;
finaltol: 1e-16; %ask for at least 16 digits for all points, regardless of singularity;
condnumthreshold: 1e300; % label no points as singular due to condition number. only due to multiplicity
securitylevel: 1; %track all paths to t=0, without truncating infinite paths.
endpointfinitethreshold: 1e12; %in case nullspace elements are large.
maxnewtonits: 3;
maxstepsbeforenewton: 0; %take a newton corrector step every single time step.
END;
INPUT

variable_group x, y, z;
function F;
F = (z^3-2)^2 +(x^2+y^2-3)^3;
END;