Tool to create IFS ( Iterated Fractals System )

You create shapes and affine transformations. To build IFS, your shapes are transformed by combination of all transformations.
By example if you create three transformations T1, T2 and T3 and that you choose 2 as level, your shapes are transformed by
T1°T1, T1°T2, T1°T3, T2°T1, T2°T2, T2°T3, T3°T1, T3°T2 and T3°T3.

You can see animation showing Von Koch's curve building from Bezier curve using 4 similarities.

Define transformation

  To define by graphic your transformation, you draw a parallelogram. This parallelogram is result of canvas in transformation, it define affine transformation.

To draw a parallelogram, you click three points and 4th point is calculated. Caution, order for your points change the transformation, left upper corner (0 0) give green point, left lower corner (0 300) give blue point, right lower corner (300 300) give red point and right upper corner give 4th vertice of parallelogram.
You can move this three points to change your transformation and move the parallelogram as other shapes. 

You can also define a transformation by typing numerical values for angle, ratio and translation ( similarity ) or for matrix ( affinity )

  When you modify, create or remove transformation, you have to click on level to see new IFS, if you modify, add or remove shapes, you see in real time new IFS.

On this example, level is 5 ... and IFS is composed by images of "olive" polygone by composite of this three transformations ( T1°T1°T1°T1°T1, .T1°T1°T1°T1°T2, T1°T1°T1°T1°T3 .............. )
Perhaps you have to wait some seconds to see it ...

Shapes to draw

Create a shape

  You can choose rectangle - circle - ellipse - polygon - polyline - Bezier's curve - pencil or text

For rectangle, picture, circle and ellipse, you click for vertice ( rectangle - picture ) or center ( circle - ellipse ) and button pressed, moving the pointer, you define the shape

For polygon, polyline and Bezier's curve, you click for vertices. Click twice on last vertice to finish.

For pencil, you move pointer, left button pressed. On mouse up, drawing is linearised.

For text, you click on canvas and ? is draw, with keyboard you can write your text. ( Delete has no effect, use Backspace to remove letter from text )
With Enter, you can define other text element.

Move a shape

  Click on shape and button pressed move your pointer. You can select many shapes by drawing a dashed rectangle around and move them.

Modify a shape

  You can modify, remove, rotate, put in foreground or background a shape or edit text

 Modify the shape

For rectangle, picture, circle and ellipse, you click on the shape, a red circle is draw, you click on it and button pressed move this circle to change dimensions and geometry of your shape.

For polygon, polyline and Bezier'curve, you click on the shape, vertices and control points ( for Bezier ) become red circles that you can move to change geometry of your shape.

Remove the shape

   Click on shape to remove. Confirm in popup window

Rotate the shape

Choose clockwise or anticlockwise and at each click on shape, it rotate from 15 degrees.

Put shape in background or foreground

Shapes are draw in order you define them. To change this order, choose icon and at each click on shape it will go up or down in array of shapes

Edit text

Click on text to select it and with keyboard modify your text.

Presentation attributes

When a shape is draw, in "Shape" on right, you can modify all presentation attributes

You can choose color or gradient for fill or stroke, opacity, stroke width. For a rectangle you can choose also radius for rounded corners.

You can choose color directly from HSL color picker for fill or stroke.
To apply this color, selct a shape and click on selected color.

You can choose a pattern to fill or stroke the shape :

You can also choose linear or radial gradient to fill or stroke your shape

From "Workspace" you can choose other colors palette. You can create your own palettes ( See in Utilities ).

For text, you can show popup window where you can modify all attributes for text. You see effect on selected text.

You can put your text on existing curve ( polygon, polyline, Bezier curve or drawing with pencil only )
Select text, click on "OK" and choose curve. You cannot remove this curve, but you can give it no color for stroke to make it invisible.

You can modify curve and text's attributes.

Save your work

  You can get blank page ( after confirmation ), save your work ( You have to give a name for file ), load existing work, save IFS as svg file and print your drawing in popup window..

Zoom and pan

  You can zoom in, zoom out, get original view and pan in four directions.

Utilities

From "Workspace" you can show / hide grid , choose size for grid, show / hide rubber bands, choose a color for background, choose other palette. You can remove color or gradient that you create.

  You can create and save your own palettes and make your group for fonts

Create new colors palette

You define color moving cross and slider, click on square to affect it the color.
Give a name for palette and save it ...