How do you quantize the fractal elements?
Where you plot what is the size of the element you plot with?
Is it infinitely small or zero? or some finite?
I gave you some of those Julia's. Remember?
Julia plots are Beautiful and Interesting.
See : https://postimg.cc/gallery/QHcFVXN
Plotted on the complex plane, each Julia is specific to a complex C .
On 8/31/2024 11:00 AM, casagiannoni@optimum.net wrote:
Julia plots are Beautiful and Interesting.
See : https://postimg.cc/gallery/QHcFVXN
Plotted on the complex plane, each Julia is specific to a complex C .
If for any complex Z , the magnitude of Z = ( Z + C ) squared
iterated n times does not exceed 2 , then Z is a point in the Julia
for C at n iterations.
If a Julia contains the origin and is connected, then C is part of the
Mandelbrot set.
See : https://postimg.cc/gallery/YqLphGg
The Mandelbrot appears to be a well defined figure with apparent
borders or boundaries MBT-1 .
Yet when one zooms in on a border or boundary, there is an
ongoing riot of complexity on all scales, MBT-1, -2, -3, -4 .
It would be nice if you gave a little credit for the ones I showed to you?
On 8/31/2024 12:08 PM, casagiannoni@optimum.net wrote:
On Sat, 31 Aug 2024 11:52:29 -0700, "Chris M. Thomasson"
<chris.m.thomasson.1@gmail.com> wrote:
On 8/31/2024 11:00 AM, casagiannoni@optimum.net wrote:Agree !
Julia plots are Beautiful and Interesting.
See : https://postimg.cc/gallery/QHcFVXN
Plotted on the complex plane, each Julia is specific to a complex C .
If for any complex Z , the magnitude of Z = ( Z + C ) squared
iterated n times does not exceed 2 , then Z is a point in the Julia
for C at n iterations.
If a Julia contains the origin and is connected, then C is part of the >>>> Mandelbrot set.
See : https://postimg.cc/gallery/YqLphGg
The Mandelbrot appears to be a well defined figure with apparent
borders or boundaries MBT-1 .
Yet when one zooms in on a border or boundary, there is an
ongoing riot of complexity on all scales, MBT-1, -2, -3, -4 .
It would be nice if you gave a little credit for the ones I showed to you? >>
... but not sure how.
Why don't you Email something.
I already showed you some of them. Remember?
On 8/31/2024 12:08 PM, casagiannoni@optimum.net wrote:
On Sat, 31 Aug 2024 11:52:29 -0700, "Chris M. Thomasson"
<chris.m.thomasson.1@gmail.com> wrote:
On 8/31/2024 11:00 AM, casagiannoni@optimum.net wrote:Agree !
Julia plots are Beautiful and Interesting.
See : https://postimg.cc/gallery/QHcFVXN
Plotted on the complex plane, each Julia is specific to a complex C .
If for any complex Z , the magnitude of Z = ( Z + C ) squared
iterated n times does not exceed 2 , then Z is a point in the Julia
for C at n iterations.
If a Julia contains the origin and is connected, then C is part of the >>>> Mandelbrot set.
See : https://postimg.cc/gallery/YqLphGg
The Mandelbrot appears to be a well defined figure with apparent
borders or boundaries MBT-1 .
Yet when one zooms in on a border or boundary, there is an
ongoing riot of complexity on all scales, MBT-1, -2, -3, -4 .
It would be nice if you gave a little credit for the ones I showed to you? >>
... but not sure how.
Why don't you Email something.
I already showed you some of them. Remember?
On 8/31/2024 12:08 PM, casagiannoni@optimum.net wrote:
On Sat, 31 Aug 2024 11:52:29 -0700, "Chris M. Thomasson"
<chris.m.thomasson.1@gmail.com> wrote:
On 8/31/2024 11:00 AM, casagiannoni@optimum.net wrote:Agree !
Julia plots are Beautiful and Interesting.
See : https://postimg.cc/gallery/QHcFVXN
Plotted on the complex plane, each Julia is specific to a complex C .
If for any complex Z , the magnitude of Z = ( Z + C ) squared
iterated n times does not exceed 2 , then Z is a point in the Julia
for C at n iterations.
If a Julia contains the origin and is connected, then C is part of the >>>> Mandelbrot set.
See : https://postimg.cc/gallery/YqLphGg
The Mandelbrot appears to be a well defined figure with apparent
borders or boundaries MBT-1 .
Yet when one zooms in on a border or boundary, there is an
ongoing riot of complexity on all scales, MBT-1, -2, -3, -4 .
It would be nice if you gave a little credit for the ones I showed to you? >>
... but not sure how.
Why don't you Email something.
I already showed you some of them. Remember?
On 9/3/2024 11:47 AM, casagiannoni@optimum.net wrote:
On Sat, 31 Aug 2024 12:59:17 -0700, "Chris M. Thomasson"
<chris.m.thomasson.1@gmail.com> wrote:
On 8/31/2024 12:08 PM, casagiannoni@optimum.net wrote:
On Sat, 31 Aug 2024 11:52:29 -0700, "Chris M. Thomasson"
<chris.m.thomasson.1@gmail.com> wrote:
On 8/31/2024 11:00 AM, casagiannoni@optimum.net wrote:
Julia plots are Beautiful and Interesting.
See : https://postimg.cc/gallery/QHcFVXN
Plotted on the complex plane, each Julia is specific to a complex C . >>>>>>
If for any complex Z , the magnitude of Z = ( Z + C ) squared
iterated n times does not exceed 2 , then Z is a point in the Julia >>>>>> for C at n iterations.
If a Julia contains the origin and is connected, then C is part of the >>>>>> Mandelbrot set.
See : https://postimg.cc/gallery/YqLphGg
The Mandelbrot appears to be a well defined figure with apparent
borders or boundaries MBT-1 .
Yet when one zooms in on a border or boundary, there is an
ongoing riot of complexity on all scales, MBT-1, -2, -3, -4 .
It would be nice if you gave a little credit for the ones I showed to you?
Agree !
... but not sure how.
Why don't you Email something.
I already showed you some of them. Remember?
Yes and I had mentioned them in a previous posting.
Let me know how you want them covered now.
Perhaps a list of the specific image designations ?
Email ? ...
Maybe my name is an image of the julias I showed you? something like
this, search for my name here:
https://paulbourke.org/fractals/juliaset/
You will find one of mine. See? Paul mentioned my name and gave proper >credit. See?
Julia plots are Beautiful and Interesting.
See : https://postimg.cc/gallery/QHcFVXN
Julia plots are Beautiful and Interesting.
See : https://postimg.cc/gallery/QHcFVXN
Julia plots are Beautiful and Interesting.
See : https://postimg.cc/gallery/QHcFVXN
Julia plots are Beautiful and Interesting.
See : https://postimg.cc/gallery/QHcFVXN
The julia's I gave you are of a higher cycle order... Takes more
iterations to see them....
The julia's I gave you are of a higher cycle order... Takes more
iterations to see them....
On 9/5/2024 12:17 PM, Chris M. Thomasson wrote:
On 9/5/2024 11:28 AM, casagiannoni@optimum.net wrote:
The julia's I gave you are of a higher cycle order... Takes more
iterations to see them....
Not sure what you're saying here.
I run my program for as many iterations as it takes to get a desired
image. Maximum iteration numbers are clearly shown on each of my Julia
images.
High cycles means it take a lot of iterations to see the details. Try
this one out when you get some time:
https://paulbourke.org/fractals/cubicjulia
Pretty high cycle...
Some other ones:
https://paulbourke.org/fractals/septagon
https://paulbourke.org/fractals/logspiral
So much great stuff as usual!
I'll have to see and work, if and when I get the time and energy.
Thanks again!
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