46 lines
1.3 KiB
Text
46 lines
1.3 KiB
Text
# Helper function: compute (x, y)
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create or replace function xy(i, a) as table (
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with recursive cte1(k,y,x) as (
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select 0 as k, 0.0::DOUBLE as y, 0.0::DOUBLE as x -- 0 or 1
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union all
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select k+1 as k, (1.0 - 2.0 * x * y) as y, (a - (x * x) ) as x
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from cte1
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where k < power(2, i)
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)
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select last(x order by k) as x, last(y order by k) as y from cte1
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);
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create or replace function compute_a(a0, i, jmax) as (
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with recursive cte2(j, a) as (
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select 0 as j, a0::DOUBLE as a
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union all
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(with xy as (from xy(i, a) )
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select 1+j as j, (a - (x / y) ) as a
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from cte2, xy
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where j <= jmax
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)
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)
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select last(a order by j) as a
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from cte2
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);
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create or replace function feigenbaum_delta(imax, jmax) as table (
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with recursive cte(i, d, a1, a2) as (
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select 1 as i, 3.2::DOUBLE as d, 1.0::DOUBLE as a1, 0.0::DOUBLE as a2
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union all
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( with atable as (select compute_a((a1 + (a1 - a2) / d), i+1, jmax) as a from cte )
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select i+1 as i,
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(a1 - a2) / (atable.a - a1) as d,
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atable.a as a1,
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a1 as a2
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from cte, atable
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where i < imax
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)
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)
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select i, d as "δ"
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from cte
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order by i
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);
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.print Feigenbaum's delta constant incremental calculation:
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from feigenbaum_delta(13, 10);
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