• December 11, 2017, 03:52:51 PM

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##### Discuss Fractalforums / Re: Sockratease missing
« Last post by Fraktalist on Today at 03:23:51 PM »
I received 2 more private message in the shoutbox 4 days later (25th october). They already sounded like he was heading into problems but that he's still fighting.

I sent emails to him, no response. Just tried again and it bounced back, "recipients inbox is full".
Then there is his website - no longer online, just a blank page. It was stilll online one or two months ago.

Not looking good.
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##### Image Threads / Re: gerrit images
« Last post by gerrit on Today at 04:57:51 AM »
Framed Julia.
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##### Kalles Fraktaler / Re: Kalles Fraktaler 2 + GMP
« Last post by gerrit on Today at 03:30:36 AM »
This location does not render correctly in 2.12.7, fine in 2.12.6.
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##### Fractal Mathematics And New Theories / Re: Newton-Raphson zooming
« Last post by gerrit on Today at 02:05:01 AM »
Here's another hopefully interesting picture.
Top-left all pixels for which ball method found a period.
Top-right what is left over after verifying with Newton method that there is a nucleus.

For distance estimate definition $$d_e = |z_n|\log|z_n|/|z'_n|$$ we have
$$d_e/2 \leq d \leq 2d_e$$ with $$d$$ the true distance to the boundary.
If R is half the pixel distance it follows that if
$$R>2d_e$$ there is a nucleus in the pixel
$$R<d_e/(2\sqrt{2})$$ there is no nucleus in the pixel
otherwise could be either way.

Middle-left shows the yes and maybe pixels. Middle right where DE is sure there is a nucleus but ball+NR didn't find it.
Bottom-left periods missed by the ball method alone, bottom-right ball false positives.
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##### Fractal Mathematics And New Theories / Re: M-set distance estimation
« Last post by quaz0r on Yesterday at 10:00:56 PM »
perhaps it is clear; im not a mathematician.  why isn't it clear to anyone else though?  in syntopia's blog post for example, there is a section "Quilez’ Approximation" where he states "I arrived at the formula above after reading Iñigo Quilez’ post about the Mandelbulb."  clearly he holds quilez in high enough regard here, yet if you look at quilez' own web page about distance estimation, you again find the formula given with no 2.

edit:  should have read further.    quilez posted on the old fractalforums, but still the language used here:

Quote from: quilez
Now, I'm missing the 2 factor, and I'm not sure why. In fact, apparently the real formula is dist = 2·|Z|·log |Z| / |dZ| and then by something called the "Koebe 1/4 theorem" we know the distance must be not more than a quarted of the previous quantity, so:

dist >= 0.5 · |Z|·log |Z| / |dZ|

Apparently the 1/4 factor holds for 3D too. The 2 that I'm missing in the numerator factor Im not sure where it comes from, probably from one of those 2^n thingies, so I would say it is related to the power of the M set indeed. In that case, the distance estimator would be

DE = (power/4) · |Z|·log |Z| / |dZ|

but Im not sure. Perhapse somebody here can confirm?

its like we're still not sure, and its still a guessing game...
and apparently he is unsure enough to have still not changed the formula on his website.
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##### Fractal Mathematics And New Theories / Re: M-set distance estimation
« Last post by gerrit on Yesterday at 09:45:06 PM »
There is clearly a typo (missing 2) in the pdf going from 3.7 to 3.8.
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##### Fractal Mathematics And New Theories / Re: M-set distance estimation
« Last post by quaz0r on Yesterday at 08:54:56 PM »
did we really achieve clarity here though?  in the pdf there is no 2..  in syntopia's blog post he states his "strong belief" that the formula is wrong and then puts a big red 2 in there...

also why is this a matter of belief at all, strong or otherwise?
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##### Fractal Mathematics And New Theories / Re: M-set distance estimation
« Last post by gerrit on Yesterday at 07:22:40 PM »
Finally some clarity, many thanks!
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##### Fractal Mathematics And New Theories / Re: Reference Point for Reference Orbit
« Last post by mrmath on Yesterday at 05:14:03 PM »
Thanks.
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##### Discuss Fractalforums / Re: Sockratease missing
« Last post by Anon on Yesterday at 05:01:20 PM »
Copied from the Shoutbox:

[21|Oct 04:57] Sockratease: Hi Christian! Our thoughts were to go with December 1st and start a 30 day countdown timer on the site beginning November 1st.

[21|Oct 04:59] Sockratease: I have the best procedures already lined up to stop all registration, posting, and uploading but still allow logging in of existing accounts so they can still access their private messages (read, but not write PMs!)

FYI
It looks like Sockratease has an email address (hidden) on FF.com.
Could Christian or a Global Mod find/see that email address and try to contact him?
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