Years ago, rkb.ulb included code that allowed the making of Mondrian-type images, but it is no longer in that file. I thought about this for a long time and decided to develop such code, though mine is totally different. (The rkb code used Trap Shape, and mine is entirely in the outside coloring.) Here’s an example of the result. Not as good as Mondrian’s, but reminiscent. And not at all fractal in nature!
alt="5fab2801e9ec4.jpg">
Mondrian8 {
::t+bhngn2tr53PuJOQc83jU+fAl3TWbDmf0T+hb37alq2Vqa3HavnW5CObcLgRGSvN/3f2AhQ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}
Use a pixel formula with Outside Coloring of Cells in jlb.ulb. The rectangle is divided into smaller rectangles (cells) using a random number generator. You have more than a billion random numbers to try, and many parameter settings, to get the subdivision that you like best.
The black lines are produced in the top layer. The lines are colored with gradient index 0, the cell interiors with index 0.333, and the outer border with index 0.667. This gradient is black around 0, and transparent otherwise.
Each cell has a number, n, and is colored with index equal to n/Nmax, where Nmax is the total number of cells. For this Mondrian-like image, each gradient is mostly transparent, and the gradient offset is adjusted to put the color in the desired cell.
How this works:
First a cell is chosen. There are three methods. (1) Random—each cell is equally likely to be chosen. (2) Larger—the likelihood of a cell being chosen is proportional to its area. (3) Largest—of the cells with the largest area, one is chosen at random. However, if the ratio of the largest cell area to the smallest cell area is bigger than the “Max ratio of areas” parameter, one of the largest cells is chosen at random.
Then the cell is divided. It can be divided into five parts, with a central rectangle and four rectangles around it, or in two parts. If into five parts, clockwise and counter-clockwise are possible. If into two parts, you can express a preference for the longer side, or for horizontal or vertical division. Finally, the division doesn’t have to be by thirds (for five parts) or by halves (for two parts), but can have some tolerance. Experiment.
Finally, after new cells are made, those that are too small, either in side length or in area, are marked and will never be divided. Because of this, the final figure may have fewer than Nmax cells.
Distances are as fractions of the horizontal dimension. Areas are as percentages of the total area.
Other colorings can be used in the cells using a Cell formula layer as masks. Unfortunately, getting the location and magnification has to be done by trial and error. Here is an example. The central cell is filled using with a simple Julia shape. (This divide into five parts is “clockwise.”)
CellsWithJulia {
::ReWSMin2trZTvtNOQY47Gw/HE8d7QS9dXwDbyutAFpAFJHa3TBMS0xsRSUQSuN+f/Ok6DLLS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}
Years ago, rkb.ulb included code that allowed the making of Mondrian-type images, but it is no longer in that file. I thought about this for a long time and decided to develop such code, though mine is totally different. (The rkb code used Trap Shape, and mine is entirely in the outside coloring.) Here’s an example of the result. Not as good as Mondrian’s, but reminiscent. And not at all fractal in nature!
Mondrian8 {
::t+bhngn2tr53PuJOQc83jU+fAl3TWbDmf0T+hb37alq2Vqa3HavnW5CObcLgRGSvN/3f2AhQ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}
Use a pixel formula with Outside Coloring of Cells in jlb.ulb. The rectangle is divided into smaller rectangles (cells) using a random number generator. You have more than a billion random numbers to try, and many parameter settings, to get the subdivision that you like best.
The black lines are produced in the top layer. The lines are colored with gradient index 0, the cell interiors with index 0.333, and the outer border with index 0.667. This gradient is black around 0, and transparent otherwise.
Each cell has a number, n, and is colored with index equal to n/Nmax, where Nmax is the total number of cells. For this Mondrian-like image, each gradient is mostly transparent, and the gradient offset is adjusted to put the color in the desired cell.
How this works:
First a cell is chosen. There are three methods. (1) Random—each cell is equally likely to be chosen. (2) Larger—the likelihood of a cell being chosen is proportional to its area. (3) Largest—of the cells with the largest area, one is chosen at random. However, if the ratio of the largest cell area to the smallest cell area is bigger than the “Max ratio of areas” parameter, one of the largest cells is chosen at random.
Then the cell is divided. It can be divided into five parts, with a central rectangle and four rectangles around it, or in two parts. If into five parts, clockwise and counter-clockwise are possible. If into two parts, you can express a preference for the longer side, or for horizontal or vertical division. Finally, the division doesn’t have to be by thirds (for five parts) or by halves (for two parts), but can have some tolerance. Experiment.
Finally, after new cells are made, those that are too small, either in side length or in area, are marked and will never be divided. Because of this, the final figure may have fewer than Nmax cells.
Distances are as fractions of the horizontal dimension. Areas are as percentages of the total area.
Other colorings can be used in the cells using a Cell formula layer as masks. Unfortunately, getting the location and magnification has to be done by trial and error. Here is an example. The central cell is filled using with a simple Julia shape. (This divide into five parts is “clockwise.”)
CellsWithJulia {
::ReWSMin2trZTvtNOQY47Gw/HE8d7QS9dXwDbyutAFpAFJHa3TBMS0xsRSUQSuN+f/Ok6DLLS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}
