# Playing with Dots

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Object: to have fun with colored dots. Seven sample projects are given below.

Contributed by: Karl Scherer (April 2016)
Open content licensed under CC BY-NC-SA

## Details

Click anywhere on the main board. The system will create one or more dots (i.e. colored disks) according to the control setting you specified on the left border.

Each newly created dot is stored and described as: • a pair of integers (i.e. coordinates and in the integral grid of the board) • a displacement {dx, dy} (which is {0,0} if the dot is placed on the integral grid) • the radius of the associated disk • the color of the dot • the color of the dot edge

A special board position called "pivot" can be marked. It is used to create rings of dots, the pivot being the center of the ring, and the "pivot radius" being its radius (see description of "actions" below).

Some notes on the given sample projects

Project 2: First a uniform pattern of dots is created with the action "create all" (and clicking the board). Since no displacement is activated, all dots are positioned on the integral lattice. Now choose action "invert all". Then the action "numbers" allows you to define the sequence numbers of the first and last dots of the colored central strips.

Now "invert sequence from...to" for the white, the turquoise, the yellow, and the red strips, and finally color the four strips with "paint sequence". (Of course you could also paint the strips first and invert them afterward.) Click action "numbers" again to hide the sequence numbers.

Project 3: No outlines are hidden because "edges on top" is selected. Together with randomly colored edges and an opacity of .8, this results in a somewhat organic effect.

Project 4: An interesting interplay between densely packed black circles and colored dots, both on the integral grid.

Project 5: A happy collection of buttons.

Project 6: An accidental piece of pop art. Note that the edge color is not black here.

Project 7: Based on project 2, using action "change size" with "all".

Project 8: Here the actions "show pivot", "set pivot", "set pivot radius", and "encircle pivot" are used (in exactly this order).

Controls

First select the project you want to work on.

The setter bar "<,>>" allows you to select the first, previous, next, and last project.

"board" selects the main board where you drop your dots. Boards available are square boards 7×7 up to 12×12, and also 12×15.

"moves" displays the number of times you have clicked the main board. "new" displays the number of dots added (or deleted) with the latest click. "dots" displays the number of dots that have been generated.

"back" allows you to go back one move. "to start" takes you all the way back to the start. "save" stores the current board position; "restore" recalls it.

Popup menus "seq from" and "to": All dots are numbered. (You can make the sequential numbers visible by selecting action "show numbers".) With popup menus "seq from" and "to" you can define a sequence of sequential numbers that has to be acted on, e.g. you can delete all dots numbered 5 to 10.

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"action" popup menu Actions with a star (*) are activated by clicking the main board. Actions without a star (*) are executed immediately.

If "* create" is active, clicking the board will create additional dots (details: see below). Note that already existing dots will stay unchanged! If "* change size" is active, clicking the board will resize some dots. The new sizes will range between radius=0 and radius="size" (slider value). The "subaction" controls which dots are changed in size. If "* paint" is active, clicking the board will color selected areas of existing dots (details: see "subaction" below). If "* paint edge" is active, clicking the board will color the edges of selected existing dots (details: see "subaction " below). If "* displace" is active, clicking the board will displace existing dots (details: see "subaction" below). If "* delete" is active, clicking the board will delete existing dots (details: see "subaction" below). If "show numbers" is active, the sequence numbers of each dot will be displayed. Click it again to switch it off. If "invert new sequence" is selected, the sequence of the dots created with the last board click will be inverted (click board to activate it). If "invert sequence from..to.." is selected, the selected partial sequence will be inverted; i.e. the last dot will become the first, and so on (click board to activate it). If "displacement={0,0}" is selected, the and values of the two displacement popup menus are set to zero. If "show pivot" is selected, the pivot is shown as a red cross with a black point at its center. Click "hide pivot" to hide the pivot. Click "set pivot to center" to place the pivot at the center of the board, which is its default position. If "* set pivot" is active, click the board to specify the position of the pivot. If "* set pivot radius" is active, click the board to specify the distance between the clicked position and the red pivot. This "pivot radius" will be used to "encircle the pivot" (see next option). Once the "pivot radius" is defined, a green cross will appear and the system will automatically progress to the "encircle pivot" option. If "* encircle pivot" is active, you can click the board to create a dot on the circle around the pivot. The distance between the clicked position and the pivot will always be the same (namely equal to the pivot radius); the system takes care of this. Thus you can easily create a ring of dots around the pivot. Select action "hide pivot" to get rid of the red and green crosses.

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"subaction" popup menu (when action "create" is active)

If "dot" is selected, clicking the board will create one dot at the clicked position. If "rnd dot" is selected, clicking the board will create one dot at a random position. If "10 rnd dots" is selected, clicking the board will create 10 dots at a random position. If "100 rnd dots" is selected, clicking the board will create 100 dots at a random position. If "row" is selected, clicking the board will create a row of dots at the clicked position (distance between dots is 1). If "file" is selected, clicking the board will create a file of dots at the clicked position (distance between dots is 1). If "sequence" is selected, clicking the board will create a dot set of length "to"–"from"+1, where the values "to" and "from" are taken from the associated popup menus. If "all" is selected, clicking the board will create dots at each grid position.

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"subaction" popup menu (when action "paint dots" is active)

If "dot" is selected, clicking the board will color one dot at the clicked position. If "rnd dot" is selected, clicking the board will color (in a new color) a dot that has been created before. If "10 rnd dots" is selected, clicking the board will color 10 randomly chosen dots that have been created before. If "100 rnd dots" is selected, clicking the board will color 100 randomly chosen dots that have been created before. If "row" is selected, clicking the board will color a row of dots at the clicked position. If "file" is selected, clicking the board will color a file of dots at the clicked position. If "sequence" is selected, clicking the board will color a file of dots at the clicked position. If "all" is selected, clicking the board will color all existing dots.

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"subaction" popup menu (when action "paint edges" is active)

If "dot" is selected, clicking the board will color the edge of the dot at the clicked position. If "rnd dot" is selected, clicking the board will color (in a new color) the edge of a dot that has been created before. If "10 rnd dots" is selected, clicking the board will color the edges of 10 randomly chosen dots that have been created before. If "100 rnd dots" is selected, clicking the board will color the edges of 100 randomly chosen dots that have been created before. If "row" is selected, clicking the board will color the edges of a row of dots at the clicked position. If "file" is selected, clicking the board will color the edges of a file of dots at the clicked position. If "sequence" is selected, clicking the board will color the edges of a file of dots at the clicked position. If "all" is selected, clicking the board will color the edges of all existing dots.

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"subaction" popup menu (when action "displace" is active)

If "row" is selected, clicking the board will displace a row of dots at the clicked position. If "file" is selected, clicking the board will displace a file of dots at the clicked position. If "sequence" is selected, clicking the board will displace the dots with sequence numbers "from" to "to". If "all" is selected, clicking the board will displace all existing dots.

The amount of displacement is given by the two displacement popup menus (dx and dy). If "random displacement" is active, the displacements will be random ( displacement between −dx and dx and displacement between −dy and dy).

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"subaction" popup menu (when action "delete" is active)

If "dot" is selected, clicking the board will delete the dot that is closest to the clicked position. If "rnd dot" is selected, clicking the board will delete a random dot. If "10 rnd dots" is selected, clicking the board will delete 10 random dots. If "100 rnd dots" is selected, clicking the board will delete 100 random dots. If "row" is selected, clicking the board will delete a dot with the same integral coordinate as the clicked position (if such a dot exists). If "file" is selected, clicking the board will delete a dot with the same integral coordinate as the clicked position (if such a dot exists). If "sequence" is selected, clicking the board will delete the dots with sequence numbers "from" to "to". If "all" is selected, clicking the board will paint all dots positioned on the integral grid.

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Note that not all action/object combinations are available!

"size" slider: defines the radius of the dots that are created by the next move (click the main board).

"displ x / y": defines the maximum displacements (in horizontal and vertical direction) off the integral grid for the randomly created dots; only relevant when random displacement is active (see "displ" toggle below).

color slider: defines the color of the dots that will be created by the next move (click the main board).

random size/displacement/color/color2: here you can decide whether action "create" creates dots of varying sizes, displacements, main colors, or edge colors.

"size" toggle: if activated, dots with random radius are created (by the "create" action and board click). The maximum size is given by the radius slider. If the toggle "size" is not activated, then all dots will have the same size, given by the "size" slider.

"displ" (displacement) toggle: if activated, dots with random displacement (from the associated grid points) are created (by the "create" action and board click). Note: The maximum displacement is given by the absolute values of the two displacement popup menus. Hence to get a random displacement, you have to set the two displacement popup menus to nonzero values first!

"col" toggle: if activated, random colors will be applied to dots (by the "create" action and board click).

"col2" toggle: if activated, edges of random color are applied to dots (by the "create" action and board click).

"edges no/yes/on top/only" setter bar: select here whether you want no edges, standard edges, the edges displayed after all dots have been displayed, or edges only.

"dashed": the edges of the dots and circles will be dashed.

"edge color": select the color of the edges of the dots and circles.

"grid": select "grid" to display an integral point grid on the board.

"op": select opacity to control how transparent the dots are.

"bg": select background color.

Hints

This Demonstration does not give you a control such that a dot is created at a random place. To simulate random placements of dots, choose a large displacement (i.e. select large values of and in the two displacement popup menus) and choose "random displacement" (choose "displ" under the "random" title) before you click the main board.

## Permanent Citation

Karl Scherer

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