Notes on the Turing-Klee Trilogy:

The Turing-Klee Trilogy:

Paul Klee marries the Turing Machine
                    -and together they take a line for a walk in Computational Space.

Images of "Trilogy" Java Applets

I. Parameter:

          link to "Parameter" Jave Applet
-The Parameter is a one dimensional variable that "moves" between two fixed limits (a minimum and a

Any change to the system needs to come from outside the system.

This basic parametrical system is visually represented in the first part of the Trilogy.

Visual lin to "Parameter" Java Applet


II. Meta-Parameter:

Visual link to "Meta-Parameter" Java Applet 
-The Meta-Parameters are Parameters that move the limits of the original Parameter -so the system
begins to show some signs of autonomy.

The visual representation in the second part of the Trilogy includes a "Turing" type memory space -
which calculates data (via simple rules) which then controls the actions of the Meta-Parametrical
          link to "Meta-Parameter" Jave Aplet

III. Parametrical Space:

Visual link to "Parametrical Space" Java
-In the third part of the work, the Parametrical Space combines Meta-Parameters to create a multi-
Dimensional "Computational Space". In this case, there are two Dimensions -but, potentially, any
number of Dimensions are possible.

With "Parametrical Space" it is the result of the process more than the process itself which is
given a visual representation. By moving in two dimensions, the point creates the line -while the
limits of the movement create a (rectangular) space. The two parameters can be interpreted as being
either Cartesian or Polar.

These parametrical interpretations create a visual repertoire of points and lines (representing the
movement) plus (filled or empty) rectangles (representing the limits of the movement. It is this
repertoire that helps create the underlying grammar for the image creation. These basic elements
can also be assigned colours by incrementing through a small "palette" built into the system -but
all options for the image generating process must be under control of data abstracted from the

With the image being used as a (limited) source of data, the entire process has the  potential to
become a sustainable (chaotic) ecology of data and process.

          link to "Parametrical Space" java Applet

The autonomy of the Meta-Parameter now manifests itself in a space
- which defines the movement of the point
- which forms the line
- which makes the drawing walk the walk.

So, the point, as it moves through space, creates the line and the line creates the image -but
these also provide the data that keeps the process alive.
          link to "Parametrical Space" Java Applet


Images of "Trilogy" Java


Conceptual Background
Technical (Presentation) Notes


To start Java Applet -click on image link

(To bring up process menu: right click on Java image  when Applet is running)
Use left mouse button to select menu options
Use browser navigation buttons to close or leave the process window


Trevor Batten, Baclayon, March 2019

Project Klee

Project Number