Figure XXa shows the timing of when goals were achieved in each trial. While the trial with the fastest progress reached the 16th goal in about 30,000 steps, the trial with the slowest progress did not yet reach the 11th goal even after 100000 steps. This indicated that a large variation existed when only 1 agent was present.
The number of inventions in each trial is shown in figure XXb. Generally, we see a repeated pattern where there is a rapid increase in invention followed by a period where there is minimal increase in invention, which resembles that of a sigmoidal function.
Figure XXc shows the number of improvements that made the circuit more efficient. In total, we see a general increase in improvements as time steps proceeds. Also, similar invention, occasionally there is a rapid increase followed by a gentle slope.
Figure XXd shows the number of cases where neither invention nor improvement occurred. The figure indicate that there is little variance within junk. This is because the number of times innovation and improvement occurred is less than the number of steps.

Comparison between group sizes

Figure XXa shows the number of goals achieved in each condition with the light line indicating the actual data and the solid line the average. The average value was displayed up to a point where no termination was present in all trials. The pattern indicated that as group size increased, so did the speed of goals achieved. Likewise, the difference between conditions became larger as steps advanced. In figure XXb, light lines represent data where the speed of size-1 is increased by the number of group size compared (which also could be interpreted as dividing the number of trials in group size-1 by the number of group size compared). Since the light line is above the solid line (which is the average of the actual data) in all conditions, the productivity of group size was lower than expected.
Similar to figure XXa, figure XXb shows the comparison within invention. The average number of inventions indicated that as group size increased, cumulative increase in invention started to resemble that of a sigmoidal shape. This indicated that as group size increased, the gentle slope seen in replications under group size-1 was quickly followed by a rapid increase. And as quicker the goals were met, the plateau in bigger group size became longer along the end of the simulation. Figure XXb also shows when the speed of group size-1 was increased. Similar to goals, the light line is above the solid line indicating that the productivity of group size was lower than expected. We also fitted the data using OLS (ordinal least square) with the power function applied through the curve_fit function from SciPy module in Python. Since the data fitted poorly in invention, it suggested that the increase in invention did not follow a power function.
Figure XXa shows the actual data and their average results from improvement in each condition. Consistent with goals and inventions, speed of improvements also increased with increase in group size similar to a gentle upward convex function. When the speed of group size-1 was increased to compare with other group sizes, the two lines seemed to overlap with one another. This indicated that the speed of improvements was proportional to that of group size. Just as in invention, we fitted the data with OLS. The results indicated that improvement was roughly proportional to the square root times the group size, but there was a pattern in which the estimated value of the index increased as the group size increased. This suggested that as the group size increased, the rate of increase of the slope became steeper. The results from OLS also suggested that the properties of invention and improvement differed. This suggested that the mechanisms of these two variables might be different.
Figure XX shows the results from junk. The accumulation of junk increased as the group size increased (figure XXa). When the speed of group size-1 was increased, the results overlapped with the increased data set.