Aaron H. "ansr23" wrote:
>
>    the reason i generally don't go any larger is because i work with
>    multiple layers so any larger file size and i'll crash my current machine.
>    there's also the rendering time        ...................     are there any
>    file size limits for software like fractal explorer or ultrafractal?

One way or another, there will always be file size limitations, regardless of the software application used.  There are several factors that should be considered when rendering large images:

  1.   The CPU/s and it/their capabilities.
  2.   Available Hard Drive space.
  3.   Amount of RAM installed and usable.
  4.   Virtual Memory allocation.
  5.   Whether rendering from the application window or using a "Render To Disk" option.

By choosing the Render To Disk approach, an image can usually be generated to create a high-resolution image with better quality than is possible from the application's window.  Which means larger images beyond the capacity of your video adapter.

Bernard Helmstetter wrote:
>
>    I was speaking in terms of pixels per inch of paper,
>    not per inch of screen.  You seem to claim that we
>    need as many pixels as we can print dots, but in my
>    opinion it is not so useful.

Printed images never do have pixels, they use "dots" of colors.  To my knowledge, nobody refers to the "dots" on printed output (paper or otherwise) as PIXELS.  Which is why there is a difference in terminology:   DPI for printing   and   PPI for rendered images.  The term  DPI is often used interchangeably with PPI, causing a lot of confusion, however, DPI refers to the resolution of a printing device.  PPI is a measurement of image resolution that defines the size of an image.

There are several thousand web pages that can help in your understanding of these differences.  Try a quick search with Google, using the following two words:   DPI  PPI

By rendering an image with more pixels than you think you may need, it will give more flexibility in the printed output.  It will allow you to resize/resample the image if necessary to accomplish anti-aliasing, and to print with a finer DPI value for a higher quality of output, without getting a really small printed image.

easy now, not everyone on these forums makes the distinction and i don't think that was directed at you

edit: to answer your question, no, they are not directly comparable - for example the change of colour space, as you mentioned, makes a direct resolution comparison impossible. as a rule of thumb a dot pitch (as it's usually given) of .28 on a monitor looks reasonably smooth, and 300dpi on a printer (varies from printer to printer of course) looks good.

If the original rendering was 1600 x 1200, then printing at different DPI values would produce the following:

    DPI         Printed Image
-------------------------------------------
   100           16"  x 12"
   200            8"   x   6"
   300          5.3"  x   4"
   400            4"   x   3"
   600          2.6"  x   2"

Pixels per inch (PPI) or pixel density is a measurement of the resolution of a computer monitor's display, related to the size of the display in inches and the total number of pixels in the horizontal and vertical directions.  PPI may also be used to describe the resolution of an image scanner or digital camera; in this context, it is synonymous with samples per inch.

The measure of pixel density is useful for calibrating a monitor with a printer; software can use the PPI measurement to display a document at "actual size" on the screen.

The apparent PPI of a monitor depends upon the screen resolution (that is, number of pixels) in use; a monitor in 800 by 600 mode has a lower PPI than the same monitor at 1024 by 768 mode.

   http://www.michaelfurtman.com/pixels.htm

   http://www.tildefrugal.net/photo/dpi.php

   http://www.shortcourses.com/pixels/printed.htm

Bernard Helmstetter wrote:
>
>    .....values of dots come from values of pixels, and in average we
>    have x pixels per dot.  The question is:  is it really necessary to have
>    x=1 to get optimal printing results, or we can we do with less?

You can do anything you choose to do, even if it is "with less".  And it is not "necessary to have x=1".  As they say, anything is possible.  But if you want QUALITY, then certain values should be followed.

A single pixel can be printed to paper and take up the space of 3-inches by 3-inches, though it may end up looking like an Andy Warhol image.  That same single pixel can be printed to paper and be just a portion of a single "dot" on the paper.  Pixels and Dots are not really comparable in the way you seem to be expressing.

You may be interested in reading this:
    http://aic.stanford.edu/sg/bpg/annual/v15/bp15-08.html


Bernard Helmstetter also wrote:
>
>    Next time I'm writing in chinese, we may understand ourselves better 

That is fine with me, I will have no problem, you may also choose any of the dialects that works best for you to communicate with.  I can also communicate in several other languages as well, if that better suits you.

Bernard Helmstetter wrote:
>
>    You are the one who has repeatedly been claiming that we
>    need as many pixels as dots.   Did I miss something?

I do not believe I stated what you claim I said.  I have been saying that pixels and dots are different, and that the number of pixels will take up a certain amount of space on the printed paper based upon the printer's DPI setting.  It is nothing more than a simple formula to follow when one knows what size they wanted the image to be printed at and the DPI value.

>
>    When I write that there is less information in a dot than in
>    a pixel, do you understand me?   Do you agree?

Well that depends on the context of how each word is used.

Literally, there is no information in a printed DOT, it is just a splash of color on the paper.

And the PIXEL (the picture element) is very context sensitive when it comes to a definition and it's use.  When we talk about a graphic image format, it usually means the smallest complete sample of an image.  And that usually takes about three bytes of storage for a single color out of the number of distinct colors that can be represented.  But it could be as little as one byte of storage, or as much as six bytes of storage, depending on the number of bits per pixel (bpp).

But a single printed DOT could have been a combination of several PIXELS in the final output, and therefore required more bytes of data to make up that DOT.