(Kalles Fraktaler) M-set zoom

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Offline gerrit

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« Reply #60 on: January 28, 2018, 06:11:36 AM »

Offline gerrit

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« Reply #61 on: February 09, 2018, 04:55:12 AM »

Offline gerrit

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« Reply #62 on: February 18, 2018, 08:46:46 AM »

Offline gerrit

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« Reply #63 on: March 10, 2018, 02:29:29 AM »
Simultaneous zooms into 16 Misiurewicz points of an embedded Julia.
http://persianney.com/fractal/v/misizoom.html

Offline gerrit

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« Reply #64 on: March 15, 2018, 02:31:05 AM »
Zoom featuring 4 embedded Julia sets by close passage to 4 mini's and using the 5th one to get the Julia set.


Click for video


« Last Edit: March 15, 2018, 05:48:25 AM by gerrit »

Offline claude

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« Reply #65 on: March 15, 2018, 05:18:20 AM »
Simultaneous zooms into 16 Misiurewicz points of an embedded Julia.
Trippy!

Zoom featuring 4 embedded Julia sets by close passage to 4 mini's and using the 5th one to get the Julia set.
I like how the density oscillates.

Offline gerrit

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« Reply #66 on: April 17, 2018, 07:20:23 PM »
Evolution of trees M-set power 3, animating location provided by dinkydau.


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Offline gerrit

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« Reply #67 on: May 23, 2018, 05:43:13 AM »
M-set for cos(z)+c can be approximated by a polynomial fractal using \( e^x \approx (1+x/p)^p \) for large \( p \).
Unlike for \( e^z + c \) which converges slowly (see my image thread for examples of large p in the billions), it seems to converge rapidly for this map. Animation shows fractal with that approximation with p going from 2 to 100 and then \( \infty \), i.e., cos(z).


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Offline gerrit

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« Reply #68 on: May 24, 2018, 12:55:53 AM »
M-set for exp(z)+c can be approximated by a polynomial fractal using \( e^x \approx (1+x/p)^p \) for large \( p \).
Animation shows fractal with that approximation with p going geometrically from 2 (just power 2 M-set) to 10000000 and then jumps to \( \infty \), i.e., exp(z).


Click for video


Offline gerrit

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« Reply #69 on: May 29, 2018, 06:51:49 AM »
Non-linear Mandelbrot zoomout.

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Offline gerrit

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« Reply #70 on: June 01, 2018, 06:24:19 PM »
Another nonlinear zoom.

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Offline gerrit

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« Reply #71 on: June 03, 2018, 09:35:36 PM »
Custom zoom to a tree.

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Offline gerrit

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« Reply #72 on: June 06, 2018, 07:56:20 AM »
Animated Julia sets. c (as in \( z \leftarrow z^2+c \)) goes from -0.75 once around the main cardioid, then once around the period 2 circle.
Top video is is slightly outside the boundary, bottom one "exactly" on the boundary.

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Offline gerrit

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« Reply #73 on: June 12, 2018, 02:26:41 AM »
Animated Julia sets for \( az^2(z-4)/(1-4z) \) with \( a \) running once around the unit circle.

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Offline gerrit

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« Reply #74 on: July 15, 2018, 02:52:13 AM »
Each frame of the animation is a mini on the real axis with period 3,4,...,199,200.


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