Getting Started:

When the program successfully starts running, you will see a display that looks like this:

Looking Around

The large window on the left titled “Weiman-Iterated Transformations” displays a red dot in the center of a blue field. The red dot is really an end-on view of a chain of 100 segments, each segment being a ball and a cylinder.

Creating and Animating Structures:

Now that you know how to maneuver your view of the structure, you are ready to roll up your sleeves and create.   The window at the upper right in the program, shown below, titled “State space controls” contains the sliders and buttons which control everything.  The window is divided into three panels, each accessible by a tab at the top.  The panel which appears on top, titled “angles” determines the curvature of the structure in all three directions of space. 

That is, consider the long chain of segments in the image above as the path of an airplane flying in a straight horizontal line.  Steering left or right is called “yaw”, up or down is called “pitch” and spinning around the propellor axis is called “roll”.  (The matrix math which expresses the transformations will be available soon in from  this LINK).  The first three sliders control pitch, yaw and roll. The sliders labelled X-rot, Y-rot and Z-rot correspond to pitch, yaw and roll.  Move the slider to watch the effect. 

The figure below shows the combined effect of X-rot and Y-rot, namely, a helix. (NOTE!! At any time you may move your viewpoint for a better view by dragging the mouse in this image as described in the “Looking Around” section above).



A displayed structure is created by pumping all the numbers from the controls into a program which converts them to the values of geometric parameters characterizing a chain of segments.  A single set of these numbers is referred to as the “state” of the system.  Since there are 10 distinct numbers to be set, each can be considered as the value of a coordinate in a 10-dimensional state space.   Transitions from one set of numbers to another can be regarded as an excursion in state space.  Later, in the section titled “State memory control” we will show how you can traverse such trajectories.

State Space Controls – Units and Details

Consider the slider labelled X-rot, which changes the angle of pitch of each segment in the structure.   Units are in cycles, that is, 360 degrees is one cycle, so .25 cycles is 90 degrees.  Dragging the “thumb” (the stubby arrow which is the movable position indicator/controller) of the slider with the mouse from the bottom to the top will bend each angle in the chain through four full rotations, i.e,  from –2 to +2 cycles.  Clicking the label, “X-rot” resets the angle to its initial value, namely, zero.

Because of the enormous range of sensitivity of the behavior of a structure to the value of its parameter, three levels of sensitivity are available to you for input. 

(Note: You must hit the “enter” key on your keyboard after typing in a number to activate your input).

As an example, type in .25 in either text field of the X-rot control, type enter, and you should see a square of sides red, green, blue and yellow.  Then click the mouse on the small arrows to the right of the upper text field and notice how the corners start smearing.  Then click above and below the slider thumb to notice how much smaller the smearing motions are.

The control mechanisms above apply to all sliders.   Descriptions of the other tabbed panels are forthcoming in a later version of this document.  Play with them anyway. 

State Memory Controls

As you spin the numbers in the “State space control” window described above, you will generate many beautiful and interesting structures resembling DNA molecules, logarithmic spirals, finite groups, snail shells, tentacles, baskets and stars.  When you try the program again, you will regret that you cannot recreate these structures and wish that you could have photographed them.  The lower right window titled “State memory control” allows you to record all settings, save them to files, animate transitions, and share files with other users.

There are three conceptual areas of relative volatility.  The “live” structures displayed in the “Weiman – Iterated Transformations” window are the most volatile, representing the exact settings of the control sliders in the “State memory control” window.  You may save any particular state by typing in a name of your choice in the “State Name” text field (NO BLANKS!) and clicking the “Record” button in the “State memory control” window below:


This saves the state in a memory which is live during the current run session of your program.   You can save any number of states and replay them by setting the value in the “Play” textfield (or clicking the up/down arrowheads on its right border).  You can see what is in memory by clicking the “Print memory” button.


The “Animate” button plays a transition (trajectory) between any two states, selected via the text fields to the right of the “Pause” button.  You can manually animate by moving the slider and other controls at the top of this window.


When you exit the program, state memory will disappear, but you can save it permanently at any time in a file on your computer by clicking the “WRITE FILE from mem” button, and following subsequent instructions for naming and locating the file.  In any subsequent run of the program, you can retrieve this file into live memory, play it, add to it and  resave it.

When you retrieve a file,  a window appears showing the contents of the file.  You mujst close this window by either:

You may download files from this website via this link.

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