Secant Animation 1

Secant Animation 1 is a tour of a large fractal created by using the secant method to find the roots of the cosine function. It is the first fractal animation created using the secant method, although it is being published after Secant Animation 2.

Eighteen key frames were used to control the viewpoint movement and zooming.

As with all videos on this channel, higher-quality versions are available at www.hpdz.net.
This video is named in honor of Caspar Wessel (1745-1818), a Danish-Norwegian mathematician who was the first to recognize the geometrical representation of complex numbers that helped them gain widespread acceptance.

Category:

Science & Technology

Tags:

• secant
• cosine
• fractal
• animation
• hpdz
• caspar
• wessel

[DeepZoomNet]

Thanks for the input about the colors. I was trying to get away from the red/green/blue/yellow/white thing. I agree there is, perhaps, an overabundance of blueness in the palette.

[DeepZoomNet]

The secant method is similar to Newton's method for finding roots, but uses two points to estimate the tangent line rather than using the derivative function to determine it exactly. A picture is worth a thousand words here... Wikipedia has a good explanation.

The cosine function is just the function whose roots we are trying to find here. The secant method can be used on any function (see my Secant Animation 2, for example).

It is an unfortunate jumble of terminology.

[FractAlkemist]

I know what secant and cosine is from trig, don't know how they relate to fractals. But its a cool vid anyway - nice techno soundtrak too. Colors too blueshifted - need some red, orange, strong yellow. Just MHO.