Difference between revisions of "Approaches"
From Techniques for computer generated pictures in complex dynamics
(Created page with "== Scanline and direct == When creating an image there are two main methods: * scanline methods: all pixels in the bitmapped will be scanned. For each pixel, the color has t...") |
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This concerns discrete dynamical systems. | This concerns discrete dynamical systems. | ||
| − | Forward iteration means that we compute z<sub>1</sub>, z<sub>2</sub>=f(z), z<sub>3</sub>=f(z<sub>2</sub>), etc... | + | Forward iteration means that we compute z<sub>1</sub>, z<sub>2</sub>=f(z<sub>1</sub>), z<sub>3</sub>=f(z<sub>2</sub>), etc... |
| − | Backward that $z_2=f^{-1}(z_1)$, etc... The solution may be non-unique. | + | Backward iteration means that $z_2=f^{-1}(z_1)$, etc... The solution may be non-unique. |
In the first approach (scanline), I nearly always used forward iteration. | In the first approach (scanline), I nearly always used forward iteration. | ||
To be discussed later, with examples. | To be discussed later, with examples. | ||
Revision as of 00:01, 28 February 2014
Scanline and direct
When creating an image there are two main methods:
- scanline methods: all pixels in the bitmapped will be scanned. For each pixel, the color has to be determined. The coordinates of the pixel are converted into mathematical parameters. Then an algorithm is run on that parameter. For instance we may have a dynamical system, the point may represent a point in phase space, whose orbit we simulate/iterate, and the color of the pixel will be chosen according to the behaviour of the orbit.
- direct drawing: points, lines or areas, are determined by their mathematical coordinates, converted into pixel coordinates, and drawn
A vast majority of my images use scanline algorithms.
Backward and forward iteration
This concerns discrete dynamical systems.
Forward iteration means that we compute z1, z2=f(z1), z3=f(z2), etc... Backward iteration means that $z_2=f^{-1}(z_1)$, etc... The solution may be non-unique.
In the first approach (scanline), I nearly always used forward iteration.
To be discussed later, with examples.
