Solar activity is studied using a cluster analysis of the time-fluctuations of sunspot number .
In the historic period ( 1850-1932 ) the cluster exponent \alpha \simeq 0.37 ( strong clustering ) for the high activity components of the solar cycles .
In the modern period ( last seven solar cycles : 1933-2007 ) the cluster exponent was \alpha \simeq 0.50 ( random , white noise-like ) .
Comparing these results with the corresponding data from laboratory experiments on convection it is shown , that in the historic period emergence of sunspots in the solar photosphere was dominated by turbulent photospheric convection .
In the modern period , this domination was broken by a new more active dynamics of the inner layers of the convection zone .
Cluster properties of the solar wind magnetic field and the aa-geomagnetic-index also support this result .
Long-range chaotic dynamics in the solar activity is briefly discussed .