OpenOffice has pretty good support for stuff like that. They just do it in a weird way. Here's how: First, set up your document so that it has the different sections/chapters labeled. For each chapter title, you must use a certain paragraph style. Press F11 to view the styles window. By default, the first level of "outlining" is the style "Heading 1". Right-click on this in the "Styles and Formatting" window (from F11) and click "modify". Modify that style to how you want it and apply it (by double-clicking) to all of your chapter titles.
Go to Tools>Outline Numbering and for the first level, change "Paragraph Style" to "Heading 1" and "Number" to "1, 2, 3, ...". This sets OOo to recognize the paragraph style "Header 1" as outline level one.
Now, for each picture you insert, select the picture and go to Insert>Caption. In "Category" type "Figure" (without quotes). Click "Options" and set the level to 1 and separator to a period. Then, the figures should appear how you want them throughout the document and the numbers will automatically update.
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I once heard the voice of God.
It said "Vrrrrmmmmm." Unless it was just a lawn mower.