To recap, the basic one-dimensional building block for the two-dimensional system we have devised consists of a two stage analogue shift register providing feedback around a transfer function circuit which generates the mapping for the iteration. The transfer function circuit consists of an amplifier having different gains for different ranges of the input voltage. It is a piecewise-linear mapping of the input voltage on to the output voltage. The possible values of input and output voltage occupy the same overall span. Thus when the output is transferred to the input by the shift register, repeated transfers do not result in the voltages going out of the overall span. This is a classic chaotic system displaying stretching (gain size greater than unity) and folding (multiple values of input for each output). In the implementations we have made the maximum gain has size about 3.
The mapping lies in the interval (0,1);(0,1) with four straight
line sections. It is sketched in Figure 2.
The most important point to note is that
we have placed a central square box such that the
iteration line (of unit slope) passes through
diagonally opposite corners. Thus the wider square
and the small square box may both be considered to
be individual autonomous one-dimensional iterating mappings.
If the motion passes from the large box to the small box,
it will stay within the small box unless there is a
method of ejecting it. This can be either by the
addition of noise, or by extending the embedded Feature inside the
small box so that it has sections which lie outside the small box
boundary. As the Feature is enlarged, a crisis point
occurs when the size is just sufficient that the
mapping within the box touches the side.
Inside the centrally placed square box of side 
(which we term The region of the Feature)
is placed the Feature, which can
be either a trap (fixed point or limit cycle)
or a snag (chaotic attractor). The snag can be
a chaotic trap.
The size of the Feature and its region can be made
arbitrarily small. The mapping is described
mathematically by the following set of equations:-
Here, F(x) is the mapping of the Feature.
Figure 2: The mapping containing the Feature.