Julia and Mandelbrot

[c***@optimum.net]

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 .

[Chris M. Thomasson]

Post by c***@optimum.net
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?

[c***@optimum.net]

On Sat, 31 Aug 2024 11:52:29 -0700, "Chris M. Thomasson"

Post by Chris M. Thomasson

Post by c***@optimum.net
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.

[Chris M. Thomasson]

Post by c***@optimum.net
On Sat, 31 Aug 2024 11:52:29 -0700, "Chris M. Thomasson"

Post by Chris M. Thomasson

Post by c***@optimum.net
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?

[c***@optimum.net]

On Sat, 31 Aug 2024 12:59:17 -0700, "Chris M. Thomasson"

Post by Chris M. Thomasson

Post by c***@optimum.net
On Sat, 31 Aug 2024 11:52:29 -0700, "Chris M. Thomasson"

Post by Chris M. Thomasson

Post by c***@optimum.net
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 mrntioned them in a previous posting.

Let me know how you want them covered now.

Perhaps a list of the specific image designations ?

Email ? ...

[c***@optimum.net]

On Sat, 31 Aug 2024 12:59:17 -0700, "Chris M. Thomasson"

Post by Chris M. Thomasson

Post by c***@optimum.net
On Sat, 31 Aug 2024 11:52:29 -0700, "Chris M. Thomasson"

Post by Chris M. Thomasson

Post by c***@optimum.net
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 mrntioned them in a previous posting.

Let me know how you want them covered now.

Perhaps a list of the specific image designations ?

Email ? ...

[c***@optimum.net]

On Sat, 31 Aug 2024 12:59:17 -0700, "Chris M. Thomasson"

Post by Chris M. Thomasson

Post by c***@optimum.net
On Sat, 31 Aug 2024 11:52:29 -0700, "Chris M. Thomasson"

Post by Chris M. Thomasson

Post by c***@optimum.net
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.

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 ? ...

Post by Chris M. Thomasson
I already showed you some of them. Remember?

[c***@optimum.net]

On Sat, 31 Aug 2024 12:59:17 -0700, "Chris M. Thomasson"

Post by Chris M. Thomasson

Post by c***@optimum.net
On Sat, 31 Aug 2024 11:52:29 -0700, "Chris M. Thomasson"

Post by Chris M. Thomasson

Post by c***@optimum.net
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 mrntioned them in a previous posting.

Let me know how you want them covered now.

Perhaps a list of the specific image designations ?

Email ? ...

[Chris M. Thomasson]

On Tue, 3 Sep 2024 13:04:26 -0700, "Chris M. Thomasson"

[...]

Maybe my name is an image of the julias I showed you? something like
https://paulbourke.org/fractals/juliaset/
You will find one of mine. See? Paul mentioned my name and gave proper
credit. See?

Not sure what you're saying here.
Is it possible to indicate which are the Julias in my list you gave me
so I can give credit. Should be able to tell by C which is clearly
indicated.

https://postimg.cc/N5L3gpGg
https://postimg.cc/qzRTNpwH
I remember those for sure. I think I gave you another one as well but I
cannot remember it right now. Too much on my mind.

I worked on those trying to get high cycle julias.

[Chris M. Thomasson]

Post by c***@optimum.net
On Sat, 31 Aug 2024 12:59:17 -0700, "Chris M. Thomasson"

Post by Chris M. Thomasson

Post by c***@optimum.net
On Sat, 31 Aug 2024 11:52:29 -0700, "Chris M. Thomasson"

Post by Chris M. Thomasson

Post by c***@optimum.net
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?

[c***@optimum.net]

Post by c***@optimum.net
Julia plots are Beautiful and Interesting.
See : https://postimg.cc/gallery/QHcFVXN

Default, 11 and possibly another were provided by Chris M. Thomasson .

[c***@optimum.net]

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.

[Chris M. Thomasson]

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...

[Chris M. Thomasson]

Post by Chris M. Thomasson

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
https://paulbourke.org/fractals/cubicjulia
Pretty high cycle...

Some other ones:

https://paulbourke.org/fractals/septagon

https://paulbourke.org/fractals/logspiral

[c***@optimum.net]

On Thu, 5 Sep 2024 12:18:56 -0700, "Chris M. Thomasson"

Post by Chris M. Thomasson

Post by Chris M. Thomasson

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
https://paulbourke.org/fractals/cubicjulia
Pretty high cycle...

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 !

[Moebius]

So much great stuff as usual!
I'll have to see and work, if and when I get the time and energy.
Thanks again!

Maybe the following might help:

[c***@optimum.net]

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. Iteration Limits are clearly shown on each of my Julia
images.

[Chris M. Thomasson]

Post by c***@optimum.net
Julia plots are Beautiful and Interesting.
See : https://postimg.cc/gallery/QHcFVXN

Default, 11 and posibly another were provided by Chris M. Thomasson .

Thank you! :^D
Btw, thank you for giving them a go in the first place. :^)

The julia's I gave you are of a higher cycle order... Takes more
iterations to see them....

[Chris M. Thomasson]

Post by c***@optimum.net
Julia plots are Beautiful and Interesting.
See : https://postimg.cc/gallery/QHcFVXN

Default, 11 and posibly another were provided by Chris M. Thomasson .

Thank you! :^D

Btw, thank you for giving them a go in the first place. :^)