*Bifurcations*: my code attempts to create nice positions for arrows and
good stream-line density.

*Gears*: I write the generating code *at a stroke* without conscious self-censorship.
I generate the animation and lost the generating codes! I am no longer able to write it again.
Someone can explain me how I did?

*Bolza*: this is a rehearsal, as a form of practice, to achieve my true goal:
the unseizable *Klein quartic*. The images is a WRML viewer snapshot, the cracks on
surface are due to my discontinuous parametrizations. The projection is the usual stereographic one,
applied to complex pair coordinates interpreted as 4D real coordinates.

The *Whitehead manifold* is not so explicit. *Inscribed square*:
with which algorithm I have calculated the square? I cheated of course:
I draw the square first, the the curve.

*Sarti Surface*: I try this file for PovRay, but the "max_gradient" factor is too high and PovRay hangs.
So, I write my c++ software for implicit surfaces. The software also exports into vrml format.
Heartfelt thanks to Claudio Montani for his teaching.
*Togliatti Surface*: made with POVRay: source code below. Note:
I like dark blue materials (must be one of my childhood disorders).

### Gallery

A Luroth Quartic - SVG File | |

Barth Decic | |

Chatelet Surface | |

Endrass Surface | |

Focal Surface - Vrml (zipped) | |

Kummer Surface | |

Sarti Surface - sarti_surface.pov - sarti surface VRML | |

Sectrix of Maclaurin | |

Togliatti Surface - togliatti_surface.pov | |

Inscribed Square - Inscribed_square.svg | |

Mountain Climbing Problem | |

Bogdanov-Takens Bifurcation - Bogdanov_takens_bifurcation.svg | |

Self Avoiding Walk (on grid) - Self_avoiding_walk.svg | |

Bolza Surface 3D Projection - Generating bolza source code | |

Circle Caustic | |

Clelies Curve | |

Clelies Curve Global | |

Involute Wheel (gears) | |

Kochanek-Bartels Splines - Kochanek_bartels_spline.svg | |

Rhodonea Curve (Rose) | |

Weierstrass Fractal Function | |

Whitehead Manifold | |

Pseudosphere |

### Final Notes

The *Pseudosphere* picture is very gimcrack. But this is the first picture I made with Blender,
after painstakingly learned to use it.

*Mountain climbing problem*: beautyfull problem! But the image is drawn in haste.
The two sides of mountain are: 1-cos(x)+(sin(x*4)*pow(PI-x,2))/16 and
1-cos(x)+(sin(x*4)*pow(x,2))/16. The peak-speed (number of peacks reached per unit of
time) is constant! As usual, made with Antigrain Graphics.