# Applets from the onlinepaper "Conformally Symmetric Circle Packings. A Generalization of Doyle Spirals".

Click HERE for help on the viewer.

You may drag the magenta colored points. The five points z1,...,z5 on the central circle are constrained to lie on the unit circle. z6 is computed from z1,...,z5 by the condition multi-ratio(z1,z2,z3,z4,z5,z6) = -1. You see that for any initinal (you can drag the center of one petal circle) radius There is a flower of six circles touching at the zi. But only for one choice of this radius the green "s-circles" are all intersecting in one point "p".

Click HERE for help on the viewer.

The three sliders are the three initial parameters of the conformally symmetric circle packings. "evolve" and "shrink" increase and decrease the number of circles shown. "reset params" resets the sliders.

Click HERE for help on the viewer.

The two sliders change the radii of the euqally labeled circles. "evolve" and "shrink" increase and decrease the number of circles shown. "reset params" resets the sliders.

How to use the Viewer

Pressing the right mouse button (or holding down the <META> key while pressing on one-button-mice systems) over the viewers main window will bring up a pop up menu with the following items

translate:
After selecting this you may drag the whole viewed configuration
scale:
After selecting this, dragging the mouse up or down will zoom in or out
rotate:
After selecting this dragging the mouse up or down will rotate the configuration
moebiustransform:
this option allows to move "0", "1", and "infinity" freely and thus apply an arbitrary Möbius transformation. These three points are shown with label (two in blue and one in red). Mouse dragging will drag the red one and a single click will step through the three points selecting the next one. You may also directly pick and drag any of them. If one holds down <CONTROL> key while dragging instead of the selected point its inverse is moved. This way one can get the point "infinity" away from infinity in the beginning: Initially only "0" and "1" are visible. Click until both are blue. Then <CONTROL>-drag until the red "inf" labeled point moves into the visible area. Then you can release <CONTROL> and drag "inf" directly.
invert on circle:
lets you invert the whole configuration on an arbitrary circle. Click dragging will open a yellow circle. Releasing the mouse button will do the inversion.
save view:
lets you store teh current view on the configuration for later return.
restore view:
lets you successively restore any previously saved views.
reset view:
resets the view to the initial settings.
move points:
In applets where points may be moved around this option makes the points draggable again when one has switched to other options inbetween.