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2011-12-15 13:42:08 +0100 | marked best answer | Newton's cubic Fractal help. Plotting Does this help? |

2011-12-14 21:44:19 +0100 | asked a question | Newton's cubic Fractal help. Plotting I'm solving newton's cubic for all the black points that occur within the fractal: I have the code: LA(x) = x - (x^3.0-1)/(3.0*x^2.0) S = solve(LA==0,x) for s in S: solve(LA == s.rhs(),x) and i want to take all those points I'm generating and plot them in a scatter plot. I think I have to use an array? Can anyone tell me exactly how I tell sage to put these points in an array then plot them? Thanks everyone for your help |

2011-12-13 20:23:42 +0100 | commented answer | Newton's cubic Math Modeling thanks. i appreciate your help. I'm still looking for an algorithm but cant seem to come up with anything! |

2011-12-13 20:22:57 +0100 | marked best answer | Newton's cubic Math Modeling I don't think this is a built-in behavior. I'd be interested in a reference for an algorithm, even! Basically, this would just be 0, anything whose tangent line sends it to zero, anything whose tangent line sends it to one of those, etc., right? If you just wanted to visualize this, you could try using some of the ideas at this ticket about Newton basins, though it wouldn't give the "black points". For a graphical way of exploring this, I would search sagenb.org for implementations of Newton's method in interactive mode. You could use (more) |

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2011-12-12 22:05:24 +0100 | asked a question | Newton's cubic Math Modeling I need to find the "black points" (where the function becomes undefined) of an equation x^3 -1 using newtons method. So the function turns out to be F(x) = x - (x^3-1)/(3x^2). Is there a way to find a majority of the points (where x is undefined as in the Newton cubic fractal photo aka the black points) using Sage? |

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