On the hopalong

The article discusses the Martin attractor (hopalong), which is a type of computational algorithm that allows generating visual structures that can have applications in graphic design or generative art. The available sources (the earliest references to Martin attractors in foreign and russian literature, modern ones - software systems for construction, web-pages of mathematical systems Maple and Wolfram), the mathematical model of the generalized Martin attractor and its special case – hopalong are analyzed. The influence of parameters on the image of hopalong is briefly considered, the irregular nature of the relationship between the image of hopalong and its parameters is shown, a number of hypotheses are put forward that require further verification. Known methods of hopalong coloring are considered and new ones are proposed. A new fractal approach to constructing hopalongs and studying hopalong as a hyperfractal is proposed. The essence of the fractal approach is briefly described, in which iterative calculations are performed for individual points of the image, with each such point corresponding to a strictly defined combination of parameter values. The construction of hopalong images based on the fractal approach is shown. The influence of the choice of statistical criterion on the hopalong image is shown. Two such criteria are shown - the average value of the jump length (the length of the trajectory divided by the number of iterations) and the area of the overall rectangle of the figure. Examples of hopalong images as sections of a hyperfractal object are shown. The methodology for further research of hopalongs for graphic design and generative art problems is outlined in general terms. Examples of problems that can be set for a student research work are given.