Simple Block-Substitution Rule Exhibits Interesting Patterns

2018 ◽  
pp. 463-479
Author(s):  
Rolf Hoffmann
Keyword(s):  
Substitution Rule ◽  
Simple Block

scholarly journals SPACE-FILLING CURVES OF SELF-SIMILAR SETS (III): SKELETONS

Fractals ◽  
2020 ◽  
Vol 28 (02) ◽  
pp. 2050028
Author(s):  
HUI RAO ◽  
SHU-QIN ZHANG
Keyword(s):  
Finite Type ◽  
Type Condition ◽  
Space Filling ◽  
Open Set Condition ◽  
Substitution Rule ◽  
Space Filling Curves ◽  
Neighbor Graph ◽  
Open Set ◽  
Self Similar

Skeleton is a new notion designed for constructing space-filling curves of self-similar sets. In a previous paper by Dai and the authors [Space-filling curves of self-similar sets (II): Edge-to-trail substitution rule, Nonlinearity 32(5) (2019) 1772–1809] it was shown that for all the connected self-similar sets with a skeleton satisfying the open set condition, space-filling curves can be constructed. In this paper, we give a criterion of existence of skeletons by using the so-called neighbor graph of a self-similar set. In particular, we show that a connected self-similar set satisfying the finite-type condition always possesses skeletons: an algorithm is obtained here.

scholarly journals Inversion of e-simple block matrices

2005 ◽  
Vol 400 ◽  
pp. 231-241 ◽  
Author(s):  
Miroslav Fiedler
Keyword(s):  
Block Matrices ◽  
Simple Block

FRACTAL TILINGS FROM SUBSTITUTION TILINGS

Fractals ◽  
2019 ◽  
Vol 27 (02) ◽  
pp. 1950009
Author(s):  
XINCHANG WANG ◽  
PEICHANG OUYANG ◽  
KWOKWAI CHUNG ◽  
XIAOGEN ZHAN ◽  
HUA YI ◽  
...  
Keyword(s):  
Short Paper ◽  
Self Similarity ◽  
Substitution Rule ◽  
Substitution Tiling ◽  
Simple Strategy ◽  
Substitution Tilings

A fractal tiling or [Formula: see text]-tiling is a tiling which possesses self-similarity and the boundary of which is a fractal. By substitution rule of tilings, this short paper presents a very simple strategy to create a great number of [Formula: see text]-tilings. The substitution tiling Equithirds is demonstrated to show how to achieve it in detail. The method can be generalized to every tiling that can be constructed by substitution rule.

Some Design Problems in Crop Experimentation. II. Multiple Blocking Systems

1995 ◽  
Vol 31 (3) ◽  
pp. 279-290
Author(s):  
S. C. Pearce
Keyword(s):  
Field Experiments ◽  
Block Structure ◽  
Design Problems ◽  
Split Plot ◽  
Alternative Approaches ◽  
Simple Block

SummaryThis paper describes the construction, usefulness and randomization of several designs for field experiments in which there is more than one set of blocks, namely: (a) row-and-column designs, in which there are two crossing sets of blocks, treatments being applied to the plots formed by their intersections; (b) row-and-column designs in which factors are applied to complete rows or complete columns, that is, criss-cross (or strip-plot) designs; and (c) split-plot designs, in which the plots in a study of one factor are used as blocks in the study of another. All are examples of a wider class of designs, with many ramifications, said to have ‘simple block structure’. It is suggested here that some of the assumptions underlying row-and-column designs are questionable. Some alternative approaches are indicated.

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