Simple Block-Substitution Rule Exhibits Interesting Patterns

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.

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Inversion of e-simple block matrices

Linear Algebra and its Applications ◽

10.1016/j.laa.2004.11.022 ◽

2005 ◽

Vol 400 ◽

pp. 231-241 ◽

Cited By ~ 4

Author(s):

Miroslav Fiedler

Keyword(s):

Block Matrices ◽

Simple Block

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V.-A SIMPLE BLOCK TRIMMER FOR THE CAMBRIDGE ROCKING MICROTOME

Journal of the Royal Microscopical Society ◽

10.1111/j.1365-2818.1933.tb01897.x ◽

1933 ◽

Vol 53 (1) ◽

pp. 25-27 ◽

Cited By ~ 2

Author(s):

Douglas P. Wilson

Keyword(s):

Simple Block

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FRACTAL TILINGS FROM SUBSTITUTION TILINGS

Fractals ◽

10.1142/s0218348x19500099 ◽

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.

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

Experimental Agriculture ◽

10.1017/s001447970002545x ◽

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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