V. Shapiro, Real functions for representation of rigid solids, Comput.-Aided Geom. Des, vol.11, issue.2, pp.153-175, 1994.

A. Gomes, I. Voiculescu, J. Jorge, B. Wyvill, and C. Galbraith, Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms, 2009.

O. Fryazinov, A. Pasko, and P. Comninos, Fast reliable interrogation of procedurally defined implicit surfaces using extended revised affine arithmetic, Comput. Graph, vol.34, issue.6, pp.708-718, 2010.

A. Pasko, V. Adzhiev, A. Sourin, and V. Savchenko, Function representation in geometric modeling: Concepts, implementation and applications, Visual Comput, vol.11, issue.8, pp.429-446, 1995.

D. Storti, C. Finley, and M. Ganter, Interval extensions of signed distance functions: iSDF-reps and reliable membership classification, J. Comput. Inf. Sci. Eng, vol.10, issue.2, p.21012, 2010.

Y. D. Fougerolle, A. Gribok, S. Foufou, and F. Truchetet, Boolean operations with implicit and parametric representation of primitives using r-functions, IEEE Trans. Vis. Comput. Graphics, vol.11, issue.5, pp.529-539, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00586480

K. Weihrauch, Computability, 1987.

L. Jaulin, M. Kieffer, O. Didrit, and E. Walter, Applied Interval Analysis with Examples in Parameter and State Estimation, Robust Control and Robotics, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00845131

C. Funfzig, D. Michelucci, and S. Foufou, Polytopebased computation of polynomial ranges, Comput.-Aided Geom. Des, vol.29, issue.1, pp.18-29, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00784002

M. Barnsley, Fractals Everywhere, 1988.

B. B. Mandelbrot, The Fractal Geometry of Nature, 1983.

J. L. Ramírez, G. N. Rubiano, and B. J. Zlobec, Generating fractal patterns by using p-circle inversion, Fractals, vol.23, issue.4, p.1550047, 2015.

A. H. Barr, Global and local deformations of solid primitives, ACM SIGGRAPH Comput. Graph, vol.18, issue.3, pp.21-30, 1984.

L. Evans, Partial Differential Equations, pp.211-223, 2010.

V. Shapiro, Semi-analytic geometry with Rfunctions, Acta Numer, vol.16, pp.239-303, 2007.

J. Allouche and J. O. Shallit, Automatic Sequences -Theory, Applications, Generalizations, 2003.

D. Hepting, P. Prusinkiewicz, and D. Saupe, Rendering methods for iterated function systems, Fractals Fund. Appl. Sci, vol.11, pp.183-224, 1991.

D. Michelucci, Reliable representations of strange attractors, Scientific Computing, Validated Numerics, Interval Methods, pp.379-390, 2001.

D. Michelucci and S. Foufou, Interval-based tracing of strange attractors, Int. J. Comput. Geom. Appl, vol.16, issue.1, pp.27-39, 2006.

A. Paiva, L. H. De-figueiredo, and J. Stolfi, Robust visualization of strange attractors using affine arithmetic, Comput. Graph, vol.30, issue.6, pp.1020-1026, 2006.

J. C. Hart, D. J. Sandin, and L. H. Kauffman, Ray tracing deterministic 3D fractals, ACM SIGGRAPH Comput. Graph, vol.23, pp.289-296, 1989.

M. N. Gamito and S. C. Maddock, Ray casting implicit fractal surfaces with reduced affine arithmetic, Visual Comput, vol.23, issue.3, pp.155-165, 2007.

O. Fryazinov and A. Pasko, Interactive ray shading of FRep objects, WSCG' 2008, Communications Papers Proc. (Václav Skala -Union Agency, pp.145-152, 2008.

K. V. Maksymenko-sheyko and T. I. Sheyko, Mathematical modeling of geometric fractals using R-functions, Cybern. Syst. Anal, vol.48, issue.4, pp.614-620, 2012.

J. Rice, Spatial bounding of self-affine iterated function system attractor sets, Proc. Conf. Graphics Interface '96, GI '96, pp.107-115, 1996.

V. Berthé and A. Siegel, Tiling associated with beta numeration and substitution, Integers, vol.5, issue.3, p.2, 2005.

V. Berthé and M. Rigo, Combinatorics, Automata and Number Theory, vol.135, 2010.

R. Martin, H. Shou, I. Voiculescu, A. Bowyer, and G. Wang, Comparison of interval methods for plotting algebraic curves, Comput.-Aided Geom. Des, vol.19, issue.7, pp.553-587, 2002.

A. Mishkinis, Extension of algorithmic geometry to fractal structures, 2013.
URL : https://hal.archives-ouvertes.fr/tel-00991384

T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms, 2009.

D. H. Bailey and R. E. Crandall, Random generators and normal numbers, Exp. Math, vol.11, issue.4, pp.527-546, 2002.

T. D. Taylor, Using epsilon hulls to characterize and classify totally disconnected Sierpi?ski relatives, Fractals, vol.23, issue.2, pp.216-481, 2015.

J. Allouche, G. Skordev, V. Koch, and T. Revisited, Fractals, vol.15, issue.4, pp.405-409, 2006.

N. De-bruijn, Algebraic theory of Penrose's nonperiodic tilings of the plane. I, Indagationes Mathematicae (Proc.), vol.84, pp.39-52, 1981.

T. T. Le, Local rules for quasiperiodic tilings, NATO ASI Ser. C Math. Phys. Sci, vol.489, pp.331-366, 1997.

K. Perlin, An image synthesizer, ACM SIGGRAPH Comput. Graph, vol.19, pp.287-296, 1985.

J. C. Hart, L. H. Kauffman, and D. J. Sandin, Interactive visualization of quaternion julia sets, Proc. 1st Conf. Visualization' 90, pp.209-218, 1990.

D. Ghazanfarpour and J. M. Dischler, Spectral analysis for automatic 3D texture generation, Comput. Graph, vol.19, issue.3, pp.413-422, 1995.