Non-linear flip-flop-1

We continue exploring ways to raise CA output. Previously output was boosted by augmenting CA-1 state . The present experiment attempts to increase output by replacing  rule- 600 with rule- 250.

delivery[1, 1, k, 2] ;
If[ p[1,prev] > p[1,now], set rule[250]; Min[++k, 70], else [set rule[600]]

CA-1 starts as an isolated process (rule = 600). At time = 20 the demand starts rising.  When demand rises, CA-1 switches between rules 600 and 250. When production{previous] > production[now]  CA-1 applies rule-250 and raises k, . When production{previous] <  production[now]  CA-1 applies rule-600. At k = 70  it starts declining.

The upper CA in the image depicts an isolated CA controlled by rule = 250.  Up to time = 20 the CA below remains isolated.  Then demand starts rising and the CA responds by switching rules as described above.  When demand = 70 CA reaches its maximal width. Then demand starts declining until reaching its minimum. At this point the experiment ends. If prolonged, CA would displayed the same pattern  again and again.

The next image depicts CA-1 tolerance and output.  Output is a 20 days running average.  As demand rises CA-1 accumulates resources and its output is low.  When demand declines   CA-1 diverts most of its resource to output and loses tolerance.

The last image depicts CA-1 tolerance accumulation relative to CA-0. CA-1[tolerance] – CA - 0[tolerance]. This is a health indicator showing that CA-1 health declines. The experiment depicts one cycle of an ongoing process which continues oscillating endlessly. Rising demand initiates a CA build up with meager output which rises when demand declines. Neither is output correlated with rising demand, nor when demand declines.

Demand triggers CA-1 out of its isolation. However CA-1 is unable to respond immediately. It first accumulates resources, and only after trigger subsides, output rises and oscillates about a constant level.

Enzymatic reaction

The tolerance curve depicts also a reaction between two molecules, A and B. At peak tolerance which is also the peak demand, A and B start to resonate, and when demand declines they form a covalent bond. Actually tolerance which is proportional to   accumulated resources  may be regarded as an energy analog.

The curve on the right depicts the effect of an enzyme which lowers the energy (tolerance) level   at which the two molecules resonate. Yet there is more to it.  The CA is a process which operates on two other processes. One supplies the molecules, and the other,  the enzyme. It is formed at  the gene from where it approaches the reaction site. After it has accomplished its task it continues to its graveyard where it is catabolized.  The curve illustrates further that the enzyme has two effects: energy saving, and reaction acceleration.

More on enzyme processes v.Citric acid cycle.


As demand rises and declines, output switches between two sates which might be regarded as on and off. It is a CA clock whose rate can be accelerated by controlling the demand.  Similar flip-flops operate in the organism accounting for threshold effects, like action potentials in nerves  or the sinus node in the heart. By lowering the upper demand the flip-flop accelerates (tachycardia) and vice versa.


delivery: [j, j-1, While[p[j-1] > set point], 2]
Argument[1]: Activated CA.
Argument[2]: Activating CA.
Argument[3]: Delivery condition.
Argument[4]: Delivery amount.
p[j]:  daily production