TED- so many amazing videos and amazing ideas. Here is a video that appeals to me on many levels.
Wednesday 17 March 2010
Sunday 14 March 2010
Pretty Newton's Basin
Having spent some time exploring many different Newton's Basins I found some pretty detail in z^4-z+1. It is amazingly detailed and just gets more detailed as you zoom in further. Click on the image below to see it full size.
and z^4+1=0 with more dynamic range scaling :
and z^4+1=0 with more dynamic range scaling :
Tuesday 9 March 2010
4th Order Newton's Basin
Took the time to add another root and coded it as yellow. For z^4+1=0 this gives
Zooming in one of the lobes illustrates a point I read in a Martin Gardner article year ago - that to go between any two colours at any level of hierarchy you need to cross the other 2 colours :
Zooming in one of the lobes illustrates a point I read in a Martin Gardner article year ago - that to go between any two colours at any level of hierarchy you need to cross the other 2 colours :
Monday 8 March 2010
Newton's Basin
Plotting the roots of z^3+1=0 and the Argand plane gives us :
And looking in more detail at the first lobe on the horizontal line we can really see the fractal nature of the plot.
Plotting z^3+z^2+1=0 gives us:
And looking in more detail at the first lobe on the horizontal line we can really see the fractal nature of the plot.
Plotting z^3+z^2+1=0 gives us:
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